MATHEMATICS. S2 Level 3/4 Course -1- Larkhall Maths Department Academy

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1 MATHEMATICS S2 Level 3/4 Course -1- Larkhall Maths Department Academy

2 Simplification & Substitution Exercise 1 (A) Simplify the following 1 2a + 3a 2 3b + 5b 3 4g + 7 g 4 9m + 2m 5 7p + 7p 6 6c + c 7 4q 2q 8 10z 7z 9 8d 5d 10 12x x 11 3a + 4a + 5a 12 4b + 3b+ 2b 13 5c + 2c + c 14 d + 3d + 7d 15 6e + 3e 7e 16 3f + 8f 9f 17 4x + 5x 7x 18 8y 3y y 19 7z + 8z 9z 5z 20 3x x + 4x x 21 7y + y 5y y 22 z + 6z + 2z 9z 23 2a 3a 24 6x 13x 25 2g 5g 26 4f + 2f 9f 27 3m 4m + 5m 28 4h 7h 3h 29 5t 4t 7t 30 2p 5p + 3p p Exercise 1 (B) Simplify the following 1 2a + 4b + 5a + 2b 2 6x + 3y + 3x + 4y 3 8m + 6n 2m + 3n 4 8a + 3b + a b 5 5x + 4y 2x y 6 6p + q 5p + 2q 7 7y + 2z 6y + z 8 s + 7t + 4s 3t 9 8x 4x + y + 6y 4x 7y 10 5a + 2b b + 3a b 8a 11 7m + n 2m 4m + 3n 12 y + 2z y + 3z + 2y 5z 13 3e + 2f e + g 2f g 14 a + b + c a + 2b c 15 7x + 3y + z 2x - y z 16 3a + b + 2a + c b + 2c 17 a + b + a b + c a 18 2m + n + p 2m + 3n 19 s + 4t + u 3s 4t u 20 p + q p q + 4r 21 3x + 2y + 5z 3x + 6y + 2z 22 7a + b + 8c 4a + 9b + 7c Maths Department -2- S2 Level 3/4 Course

3 23 8e + f + 6g 5g + 2f + 3e 24 9s + 7t + u 7t u 9s 25 4a + 2b 2a 5b 26 7m 4n + 2m 4n 27 4w 3z 6w 9z 28 2j 4k 6j 5k 29 5p 2q 6r + 2p 4q 7r 30 a 2b 3c 4a 5b 6c Exercise 1 (C) Simplify the following 1 3a 2 + 4a 2 2 6m 2 + 7m 3 9q 2 + q 2 4 5r 2 2r 2 5 6w 2 2w 2 6 7x 2 x 2 7 3a 2 + 4b 2 + 5a 2 b 2 8 6p 2 + 4q 2 3p 2 + 2q 2 9 3ab 4ab 10 6xy 3yx 11 3a 2 + 4a a 2 5a 12 7m 2 + 3n 2 4m 2 5n ab + 4bc 5ab 6bc 14 3a 2 + 5a 7 6a 2 4a b 2 6b +1 5b 2 + 6b g 2 + 2gh 7h 2 5g 2 + 6hg 2h m 3 + 2m 2 3m 7 + 2m 3 m 2 7m xy 3xz 2yz + 3zy 4zx 3yx x 2 3y x 2 y xyz 4x 2 z + 2xz 2 7zyx 4zx 2 + 3z 2 x Exercise 2 (A) Simplify the following 1 2 a 2 4 b 3 6 c 4 7 d 5 20 f 6 5 h 7 8 c 8 9 s 9 10 n 10 9 p p q x a g b m f w z S2 Level 3/4 Course -3- Maths Department

4 Exercise 2 (B) Simplify the following 1 a b 2 h g 3 j k 4 m n 5 w y 6 t s 7 e f 8 p q 9 k g 10 w z 11 a a 12 b b 13 u u 14 m m 15 r r 16 2 a b 17 6 c d 18 8 m n 19 3 y z 20 9 t v 21 3 a 2 b 22 5 m 3 n p q 24 5 x y a 5 b 26 2 y 5 z 27 4 a 3 b 2 c 28 6 m 2 n 2 p 29 3 p q r 30 4 a b 3 c 31 3 a a 32 4 b b 33 6 m m 34 7 y y 35 8 z z 36 2a 4b 37 5y 3z 38 7m 2n 39 3w 4y 40 6s 3t Exercise 2 (C) Simplify the following 1 2a 2b 5c 2 3x 2y 4z 3 5t 3u 5v 4 2c 4b 5a 5 6z y 3x 6 4x 5z y 7 2p q 4r 8 ½s 6t 2u 9 8m ½n 3p 10 ⅓p 12q r 11 9a 7b 2c 12 ¼y 32z 13 p 20q 14 2x 3x 15 4y 5y 16 3z z 17 2x 3y 5x 18 2x 3y 5y 19 3p 4p 5p 20 6g 3g 4g Maths Department -4- S2 Level 3/4 Course

5 Exercise 3 (A) Multiply the brackets 1 2(x + 3) 2 3(x 4) 3 4(x + 7) 4 5(y 2) 5 6(t + 3) 6 7(a 4) 7 8(c + 10) 8 9(q 5) 9 10(y + 5) 10 5(t 4) 11 6(z + 8) 12 3(r + 6) 13 2(y 5) 14 9(d + 7) 15 5(m + 2) 16 3(x 3) 17 4(q 5) 18 5(e + 1) 19 4(u 8) 20 8(j + 3) 21 3(2m + 4) 22 5(3r 5) 23 7(5y 8) 24 4(3d + 5) 25 7(2t 9) 26 3(5z 4) 27 7(3g 6) 28 8(2r 1) 29 4(5f 4) 30 6(3t 7) Exercise 3 (B) Multiply the brackets 1 5(2x + 3y) 2 4(2a 3b) 3 6(4p 5q) 4 8(2g + 5h) 5 7(5m 12n) 6 6(3p + 4q) 7 2(3k 4l) 8 4(7e 4f) 9 10(3y 4z) 10 6(5a + 6b) 11 3(4t 5s) 12 9(6i 8j) 13 5(p + 2q + 3r) 14 4(5m 2n + 3p) 15 3(4x + 5y 7z) 16 4(x2 + 3x + 1) 17 8(y 2 + 3y 7) 18 3(2x 2 + 5x) 19 5(4y 2 + 3y 4) 20 2(3x 2 + 4y 2 ) S2 Level 3/4 Course -5- Maths Department

6 Exercise 3 (C) Multiply the brackets 1 x(x + 3) 2 x(x 4) 3 x(x + 7) 4 y(y 2) 5 t(t + 3) 6 a(a 4) 7 c(c + 10) 8 q(q 5) 9 x(2x + 3) 10 y(5y 8) 11 p(2m + 6) 12 c(3d + 5) 13 m(5n 20) 14 y(3x + 4) 15 s(2t 3) 16 x(2x + 3y) 17 a(2a 3b) 18 p(4p 5q) 19 g(2g + 5h) 20 n(5m 12n) 21 x(3p + 4q) 22 x(3k 4l) 23 x(7e 4f) 24 y(3y 4z) 25 b(5a + 6b) 26 t(4t 5s) 27 i(6i 8j) 28 p(p + 2q + 3r) 29 m(5m 2n + 3p) 30 y(4x + 5y 7z) 31 x(x 2 + 3x +7) 32 y(y 2 + 5y 9) 33 x(y 2 + 3y 4) 34 x(2x 2 + 3x 5) 35 a(2a 2 + 3ab + b 2 ) 36 2x(3x 2 + 4x 7) 37 4a(3a 2 + 2a 7) 38 3x(4x 2 + 2xy + y 2 ) 39 3x 2 (4x + 2) 40 2xy(4x 2 3y) 41 ½x(6y - 4z) 42 ⅓x(6y + 9) Exercise 4 (A) Multiply the brackets and simplify 1 3(x + 3) + 4(x +1) 2 5(a + 3) +2(a + 2) 3 6(x + 5) + 4(x + 2) 4 9(x + 3) + 4(x + 8) 5 2(q + 3) + 5(q + 2) 6 3(2x + 4) + 5(3x + 1) 7 6(2x + 3) + 4(3x + 1) 8 5(2x + 4) + 3(4x + 3) 9 6(2b + 1) + 3(5b + 4) 10 8(2c + 1) + 3(4c + 5) 11 3(2x + 1) + 4(2x 3) 12 4(3r + 2) + 5(2r 4) 13 3(4f 2) + 5(2f 4) 14 5(2w 6) + 2(3x 8) Maths Department -6- S2 Level 3/4 Course

7 15 6(2t 4) + 4(3t 2) 16 9(3g 4) + 4(3g + 2) 17 5(4d 7 ) + 3(2d 8) 18 7(3v 1) + 4(7v 5) 19 12(2u 5) + 4(6u 1) 20 4(3k 7) + 5(2k 3) Exercise 4 (B) Multiply the brackets and simplify 1 2(3x + 4y) + 3(5x + 2y) 2 4(2x + 3y) + 2(3x + y) 3 5(4x + 3y) + 3(2x 3y) 4 4(5x + y) + 3(x y) 5 2(x + 3y) + 5(x y) 6 4(2x + y) + 2(3x 2y) 7 6(2m + n) + 3(n 4m) 8 5(p + 2q) + 2(p 4q) 9 8(2a + 3b) + 3(b 5a) 10 2(y + 2z) + 4( y z) 11 3(r + s) 2(3r + 2s) 12 5(p + 2q) 3(2p 3q) 13 3(7s + u) 2(u 5s) 14 4(2a + 3b) 5(b a) 15 6(5m + 2n) 2(6n 15m) 16 4s + 3t 2(t 2s) 17 8x + 4y + 5(y x) 18 6e + 2f 3(5f 2e) 19 6(m + 2n) 12n 6m 20 8(3m + 5k) 14m + 2k 21 5(a + 7b) 35b + 5a 22 2(6p + 3q) 3(q 4p) + 5(p +q) 23 3(2a + 3b) 4(2b 5c) + 2(10c 3a) 24 4(3x + 5y) 2(4z 10y) + 8(x z) Exercise 4 (C) Multiply the brackets and simplify 1 3a(2b + c) + 3ab + 4ac 2 4x(2y + 3z) + 3xy 2xz 3 m(3p + q) + mq mp 4 5a(2x + y) 3ax 2ay 5 6st + 3s(u 2t) 6 5az + 2a(3y z) 7 2x(3y + 4z) + 3x(y 2z) 8 5s(2u + 5v) + 2s(u 10v) S2 Level 3/4 Course -7- Maths Department

8 9 7m(2x + y) + 3m(y 4x) 10 3a(4b + 2c) + a(c 8b) 11 5x(y + 4z) + 2x(y 10z) 12 4a(b + 3c) + 3a(b 4c) 7ab 13 x(x + 3) + x(x + 4) 14 x(x + 6) + x(x 2) 15 2x(x + 3) 3x(x + 1) 16 x(x² + 4x + 2) + x(x² + 5x + 7) 17 x(x² 5x + 3) + x(x² + 8x 5) 18 x(x² 4x 6) (x² 6x 9) 19 x(x² + 6) x(x² 4x + 2) 20 x(x² 3) + x(x² 4x + 5) 21 x(x² + x 4) x(x² 2) 22 x(2x² + 3x + 1) + x(3x² 3x + 2) 23 2x(x² + 3x + 8) + 3x(x² + x 4) 24 5x(2x² 6x + 2) 2x(4x² 2x + 5) 25 3x(4x² 2x + 1) + 5(x² + 3x 2) 26 2x(7x² 3) + 3(x² + 2x 1) 27 4x(2x² 3x + 1) 2(x3 4) + 9x 28 5x(x² + 2x 3) + x(x 4) 6x 29 4(2x² + 7x 4) 2x(4x + 3) x²(3x 2) 3x(x² 2x) 4x² 31 x²(2 5x) + x(5x 3 2x + 4) Exercise 5 (A) Find the value of the following expressions when x = 4 and y = 2 1 3x 2 4y 3 6x 4 7y 5 8x 6 10y 7 2x + y 8 3x + 2y 9 4x 7y 10 6x 5y 11 10x + 3y 12 5x y 13 7x + 7y 14 2x 4y 15 xy 16 4xy 17 6yx 18 5xy 19 3xy + 2x 20 4xy 2y Maths Department -8- S2 Level 3/4 Course

9 Exercise 5 (B) Find the value of the following expressions when a = 3, b = 2, c = 1 and d = 0 1 3a + 2b 2 4a 3c 3 5a + 2b + 3c 4 5a + 3d 5 5b 3c 6 4a + 3b + 2c + d 7 5a 4c 8 6b + 2c + 3d 9 5b 4c 10 7a 5b 11 ab 12 bc 13 cd 14 a 2 15 b 2 16 c 2 17 d a b d ab + 4cd 22 6ac 2bd 23 5a 2 3bc 24 abc 25 2bcd 26 4a 2 b 27 6ab a 2 3b a b (a + b) 32 5(a c) 33 2(a + b) 34 5(b a) 35 4(c b) 36 7(c- a) Exercise 5 (C) If m = 2, t = 2, x = 3 and y = 4 work out the values of 1 2m 2 2 (2m) 2 3 2t 2 4 (2t) 2 5 (3y) 2 6 m x m 2 + xt 9 my 2 10 (mt) 2 11 (xy) 2 12 (xt) 2 13 yx 2 14 m(t + x) 15 y(m + x) 16 t(2m + y) 17 m 2 (y x) 18 t 2 (x 2 + m) S2 Level 3/4 Course -9- Maths Department

10 Direct Proportion Exercise 1 (A) 1 If 5 books cost 15, find the cost of 8. 2 If 7 apples cost 63p, find the cost of If 4 batteries cost 180p, find the cost of 7. 4 If 5 bottles of beer cost 2 45, find the cost of Toy cars cost 3 36 for 8. Find the cost of 10 cars. 6 Crisps cost 1.32 for 12 packets. Find the cost of 20 packets. 7 Stair carpet costs 78 for 12 m. Find the cost of 15 m. 8 The total weight of 7 ceramic tiles is 1750 g. How much do 11 tiles weigh? 9 A machine fills 2000 bottles in 10 minutes. How many bottles will it fill in 7 minutes? 10 The total contents of 8 cartons of fruit drink is 12 litres. How much fruit drink is there in 3 cartons? 11 Find the cost 15 cakes if 9 cakes cost Find the cost of 7 screws if 20 screws cost Pencils cost 75p for 3. How much will a dozen cost? 14 8 bars of soap cost How much will 12 bars cost? 15 A car travels 456 km on 40 litres of petrol. How far should it go on a full tank of 60 litres? books weigh 9 kg. How many books would weigh 6 kg? dollars are exchanged for How much are 80 dollars worth in? 18 A hotel charge for 5 days was 115. What would the charge be for 8 days? articles cost Find the cost of 36 of the same articles. 20 A firm s weekly wage bill for 350 employees is At the same average wage, what would be the weekly bill for 250 employees? 21 One week a licensed grocer bought 15 bottles of wine for What would he pay the next week when he ordered two dozen similar bottles? Maths Department -10- S2 Level 3/4 Course

11 22 A boy takes 150 steps in walking 120 metres. How far would he go in taking 250 steps? 23 Five cans of beer cost Find the cost of seven cans. 24 A man earns 280 in a 5-day week. What is his pay for 3 days? Exercise 1 (B) 1 A machine takes 20 seconds to make 8 coins. How long does it take to make 50 coins? 2 A plane flies 50 km in 15 minutes. How long will it take to fly 300 km? 3 If 8 pencils cost 56p, how many can be bought for 70p? 4 6 pineapples can be bought for How many can be bought for 5 20? 5 If 20 m 2 of carpet costs 150, what area of carpet can be bought for 90? 6 Oranges cost 1 68 for 12. How many can be bought for buys 120 Belgian francs. What is the price in pounds of a bus trip advertised at 105 francs? 8 Oranges cost 1.40 per dozen. Find the cost of 27 oranges two-pence coins placed in a row measure 13 metres. What would 75 coins measure? 10 A stack of 350 sheets of paper is 2.1 cm high. How high would 500 sheets stand? Indian rupees are worth 6. Find to the nearest rupee how many rupees you get for Swiss francs can be exchanged for 4. What are 104 Swiss francs worth in British money? (to the nearest penny). 13 A car uses 10 litres of petrol in 75 km. How far will it go on 8 litres? 14 A wire 11 cm long has a mass of 187 g. What is the mass of 7 cm of this wire? 15 A shopkeeper can buy 36 toys for What will he pay for 120 toys? S2 Level 3/4 Course -11- Maths Department

12 16 7 cycles cost 623. a What is the cost of 3 cycles? b How many cycles can be bought for 979? pens cost a What is the cost of 15 pens? b How many pens can be bought for 17? 18 A car travels 210 km on 30 litres of petrol. How much is needed for a journey of 245 km? 19 A light aircraft flies 375 km on 150 litres of fuel. How much fuel is needed for a journey of 500 km? 20 A tank travels 140 miles on 40 gallons of fuel. How much fuel is needed for a journey of 245 miles? 21 A 600 cm 2 pane of glass costs 25. a What area of glass costs 52? b Calculate the cost of a pane of glass of area 750 cm cm 3 of lead weighs 3390 g. Calculate a the weight of 500 g of lead. b the volume of lead that weighs 5085 g. 23 A 250 ml tin of varnish will cover 4 5 m 2. a What area will a 450 ml tin cover? b Calculate the volume of varnish needed to cover an area of 3 6 m A tree s shadow is proportional to its height. A tree 12 m tall casts a shadow of 18 m. Calculate the length of the shadow of a 10 m tall tree. Maths Department -12- S2 Level 3/4 Course

13 Exercise 1 (C) 1 2½ m of metal tube cost Find the cost of 7½ m. 2 3¼ kg of sweets costs Find the cost of 4½ kg. 3 The cost of a phone call lasting 3 minutes 30 seconds was 52 5 p. At this rate, what was the cost of a call lasting 5 minutes 20 seconds? 4 80 cm 3 of calcium weigh 120 g. a Calculate the weight of 60 cm 3. b What volume of calcium weighs 270 g? 5 This is a recipe for 6 scones. 110 g self raising flour 20 g butter 750 ml milk 1 tablespoon caster sugar How much of each ingredient is needed to make 15 scones? 6 Francis stores holiday snaps on his computer. His 24 photos take megabytes of memory. How much memory would a film with 36 photos need, assuming that the memory requirement is directly proportional to the number of photos cm 3 of mercury weigh kg. Calculate a weight of 350 cm 3 b the volume of 7 5 kg of mercury, correct to 1 decimal place. 8 At lunchtime it takes the canteen 15 minutes to serve 120 pupils in Danielle s year. Another year group has 16 more pupils. How much longer should it take to serve them? 9 It takes Joanne 2 hours to fly 688 miles from Rome to Paris. At the same speed how long would it take her to fly from Rome to London, which is an extra 220 miles away? Give your answer correct to the nearest minute. S2 Level 3/4 Course -13- Maths Department

14 10 The telephone directory for Graham s area weighs 1 95 kg and has 1600 pages. How much, correct to 3 significant figures, would you expect a directory with a 100 more pages to weigh b 100 fewer pages to weigh? 11 A girl makes a model of a ship which id 576 ft long and has one mast 54 ft high. If the length of the model is 4 feet, what length must she make the model mast? 12 In his will a man left each of his employees a legacy proportional to the number of years he had been employed by his firm. An employee with 35 years service received How many years service had an employee who received Travelling at 60 mph a train takes a certain time to do a journey of 400 miles. How far would an aeroplane travelling at 330 mph go in the same time? 14 If the cost of carriage of 35 tons for a certain distance is 1540, what weight can be carried the same distance for It is estimated that 2 tons of coal occupy 81 cu ft. How many tons of coal are there in a stack of coal 15 ft long, 12 ft broad, and 9 ft high. 16 A fitted carpet for a room 4 m by 3 m costs How much will the same kind of carpet cost for a room 5 m by 2 m? 17 In order to measure the height of a lamp post, a boy measures the lengths of the shadows cast by the lamp post and by a stick, 3 ft 8 in high. He finds the lengths of the shadows to be 8 ft 9 in and 2 ft 9 in respectively. Find the height of the lamp post. 18 A clock is wound up on Saturday at am and set to the correct time. At 6.30 pm on the following Wednesday it is 6½ minutes slow. What will be the time on the clock at am on the following Saturday? Maths Department -14- S2 Level 3/4 Course

15 Inverse Proportion Exercise 2 (A) 1 If 6 men build a wall in 10 days, how long will it take 4 men? 2 If 8 men build a wall in 3 days, how long will it take 6 men? 3 If 10 men build a wall in 7 days, how long will it take 7 men? 4 If 6 men dig a trench in 6 days, how long will it take 9 men? 5 If 40 women complete a job in 21 days, how long will it take 7 women? 6 If 24 women complete a job in 39 days, how long will it take 36 women? 7 If 18 women complete a job in 17 days, how long will it take 34 women? 8 If 15 men can build a wall in 6 hours, how long will it take 5 men? 9 If 6 men can dig a trench in 12 hours, how long will it take 24 men? 10 4 men can build a shed in 9 hours. How long would it take 6 men? 11 If 4 pipes empty a bath in 1 hour, how long will it take 2 pipes? 12 If 1 tap fills a bath in 30 minutes, how long will it take 2 taps? 13 A ship has enough food to supply 600 passengers for 3 days. How long would the food last for 300 passengers? 14 A farmer has enough hay to feed 8 horses for 2 days. How long would the hay last for 2 horses? 15 8 people can unload a ship in 15 hours. How long will it take 3 people? 16 A farmer employs 12 men to do a job in 10 days. How long would it have taken 5 men? 17 A bridge was painted by 8 men in 6 days. How long would it have taken 12 men? 18 4 men can do a job in 12 hours. How many men would it take to do the job in 2 hours? 19 6 women can do a job in 8 hours. How many women would it take to do the job in 6 hours. S2 Level 3/4 Course -15- Maths Department

16 20 Usually it takes 5 hours for 12 men to do a job. How many men are needed to do the job in 2 hours? Exercise 2 (B) 1 A garrison has enough food to last 1000 soldiers for 21 days. How long will the food last for 1400 soldiers? 2 A ship has sufficient food to last 900 people for 4 weeks. How long will the food last for 1200 people? 3 If a quantity of food can last 20 people for 6 days, how long would it last 30 people? 4 If a 700 watt microwave oven took 4 minutes to cook a piece of meat, how long would it take an 800 watt microwave to cook the same meat? 5 A car travelling at 80 km/h completes a certain journey in 60 minutes. How long would it take for a car travelling at 120 km/h? 6 A car travelling at 60 km/h completes a journey in 90 minutes. How long would it take for a car travelling at 180 km/h? 7 Six friends each pay 70 towards renting a ski chalet. At the last minute two more pals are invited on the holiday. if the cost is shared equally, how much will each of them pay? 8 Nine teams each of four pupils enter a quiz. They are reorganised into six teams. How many will be in each team now? 9 At Highmoor School there are 8 lessons of 35 minutes each day. They change to a new timetable of 7 lessons a day. If the total teaching time remains the same how long is each lesson with the new timetable? 10 Comfy Coaches have two sizes of coach. The larger has 72 seats and the smaller 48 seats. To take fans to an away match they reckon they need exactly eight of the larger coaches. How many small coaches would be needed for the same number of fans? Maths Department -16- S2 Level 3/4 Course

17 11 A piece of land can be divided into 20 individual allotments each with an area of 120 m 2. It is decided to increase the number of allotments to 24. Calculate the area of each of these allotments. 12 Five lottery winners each received If the same amount was shared between seven winners, how much would each person receive? 13 Eight friends rent a caravan for a fortnight s holiday. They each agree to pay One of them has to drop out, leaving seven of them to share the same bill. How much does each of them have to pay? 14 Main Street High School holds a monthly lottery for charity. In January two winners each receive 450. In February the total prize money is the same. If there are three winners how much does each one win? 15 Mike takes on the challenge of walking from John O Groats to Land s End. His target is to average 20 miles a day and that will mean a total walk of 42 days. If he averaged 24 miles a day, how many days would it take? 16 A team of 14 relay runners plans to run between Glasgow and Fort William. Each of them will run 20 km. They recruit two more runners to share the distance. How far will each member run now? 17 Trendy Textiles Plc give the workface of 60 employees a Christmas bonus of 250 each. The following year the total bonus remains the same but there are ten fewer employees. How much is each worker given? 18 Gill has enough food to last her five horses for 12 days. How many days will the food last if the number of horses is: a increased by one b decreased by one? 19 When the speed of a car is 24 mph, a certain journey takes 80 minutes. What must the speed be for the same journey to take 60 minutes? 20 A ship has enough coal in its bunkers to last 6 days, if it uses 105 tons per day. If it uses 140 tons per day, how long should the coal last? S2 Level 3/4 Course -17- Maths Department

18 Exercise 2 (C) 1 A journey takes 6 hours travelling at 80 km/h. How long would the journey take at 100 km/h? 2 If 45 workers can complete a job in 12 weeks, how many extra workers would it take to finish the job in 10 weeks? 3 A journey takes 4½ hours at 70 mph. On the return journey the average speed is 60 m.p.h. How much longer does the return journey take? 4 If 20 people take 7 days to harvest crops, how many days less would it take 35 people? 5 A farmer can feed 60 cattle for 8 weeks. If he sells 20 of the cattle how much longer will the feeding stuff last? 6 A journey takes 12 hours at 75 km/h. How much longer would the journey take at 60 km/h? 7 A plane flies for 8 hours at 330 m.p.h. If the plane did the same journey at 440 mph how much less time would it take? 8 A contract takes 189 men 54 days to complete. How much longer would it take 126 men? 9 At a scout camp there is enough food for 160 boys for 12 days. If 40 boys fewer than expected turn up, how much longer would the food last? 10 A man walks for 8 hours at 5 m.p.h. Had he walked at 4 m.ph. how much longer would he have taken? 11 Four lucky people share the lottery roll-over. They each get If one more person had shared the prize, how much less would each person have received? 12 At an average speed of 80 km/h, Barbara can drive from Glasgow to Edinburgh in 54 minutes. How much time would it save if she could increase her average speed by 10 km/h? Maths Department -18- S2 Level 3/4 Course

19 13 A container of shampoo will fill 800 small bottles each of 60 ml. a How many large 250 ml bottles could be filled from the container? b The container will fill 320 medium sized bottles. Calculate the volume of a medium sized bottle. 14 A set of bookshelves can hold 240 books of an average width of in. How many books of an average width of in will the same bookshelves hold? 15 Water, 3 ft 6 in deep in a rectangular tank, area of base 240 sq ft, is run into a tank, area of base 288 sq ft. What is the depth of the water in the new tank? 16 A man wishes to complete a journey in hours. Travelling at 36 mph for the first half of his journey, he takes 50 minutes. By how many miles per hour must his speed be increased if he is to complete the journey in time? 17 A contractor undertakes to do a certain job in 12 days. He employs 50 men, but finds that after 8 days only half of the work is done. How many men will he require to have working at the job during the remaining time to complete the work in time? 18 A builder contracts to complete a job in 48 days, and employs 14 people to do so. After 16 days the work is held up for 11 days by bad weather. How many extra people would now be needed to finish the job on time? S2 Level 3/4 Course -19- Maths Department

20 Speed, Distance and Time Exercise 1 (A) How many hours and minutes are there between the following times? am and 9.15 am am and am pm and 2.30 pm pm and 5.45 pm pm and 9.20 pm pm and pm am and 4.45 am am and 6.30 am am and 9.00 am am and pm am and am am and pm pm and 1.35 pm pm and 4.05 pm pm and 5.15 pm pm and 6.25 pm pm and 8.05 pm pm and pm pm and pm am and 3.15 am. 21 Jonathon watches a film on television. It starts at 9.25 pm and finishes at pm. How long did the film last? 22 Archie watches the big game on TV. The programme starts at 7.30 pm and finishes at pm. How long did the programme last? 23 The am train from Glasgow arrived in Edinburgh at am. How long did the journey last? 24 Justin goes out jogging from 7.30 pm until 9.00 pm. For how long was he jogging? 25 Derek has to travel each day as part of his job. One week in December he had the following journey times. Find his journey time each day. Monday Depart 7.30 am Arrive am Tuesday Depart pm Arrive 3.25 pm Wednesday Depart 8.50 am Arrive pm Thursday Depart 3.20 pm Arrive 5.05 pm Friday Depart 8.55 am Arrive 3.20 pm Maths Department -20- S2 Level 3/4 Course

21 Exercise 1 (B) How many hours and minutes are there between the following times? am and pm pm and 2.15 am am and am am and pm am and 2.18 pm pm and 3.44 pm pm and 4.08 pm pm and 7.52 pm am and 8.43 am am and 8.43 am. 11 Sean takes the overnight train from London to Dundee. The train leaves London at 9.30 pm and arrives in Dundee at 6.15 am the following morning. How long does the train journey last? 12 The following programmes were shown on a TV channel one evening pm News Report 6.30 pm Local News 6.45 pm Scenes from Soaps 7.30 pm European Football Live pm Film The Curse of Pi pm Evening News pm Wee Brother a How long does Scenes from Soaps last? b Brian plans to watch Scenes from Soaps, European Football, and also the film. How long does he plan to spend watching television? c Due to extra time in the football, all programmes are delayed by 50 minutes. When will Wee Brother start now? S2 Level 3/4 Course -21- Maths Department

22 13 Bert is working on night shift. He starts work at pm and finishes at 7.25 am the next day. How long does he work? 14 Martin has a DVD which lasts for 135 minutes. If he starts watching it at 8.50 pm, when will it finish? 15 Amy has to check in at the airport at 3.20 pm. If it takes her 4 hours 30 minutes to travel from home to the airport, what is the latest time she can leave home? 16 Shona has an interview at am. She has allowed 2 hours 30 minutes to travel from her home to the venue for the interview. What is the latest time she can leave home to be in time for the interview? Exercise 2 (A) Find the times taken for each of the following journeys 1 Start 9.00 am Finish am 2 Start 2.00 pm Finish 5.00 pm 3 Start 7.00 pm Finish pm 4 Start 7.30 am Finish am 5 Start am Finish am 6 Start 8.00 am Finish am 7 Start 2.00 pm Finish 6.30 pm 8 Start 6.30 am Finish am 9 Start 2.15 pm Finish 5.45 pm 10 Start 3.15 pm Finish 8.30 pm 11 Start 0900 Finish Start 1100 Finish Start 1500 Finish Start 1630 Finish Start 2030 Finish Start 1615 Finish 1815 Maths Department -22- S2 Level 3/4 Course

23 17 Start 1730 Finish Start 0030 Finish Start 0815 Finish Start 1915 Finish 2230 Exercise 2 (B) Find the times taken for each of the following journeys 1 Start 9.15 am Finish am 2 Start 2.05 pm Finish 5.09 pm 3 Start 7.31 pm Finish pm 4 Start 7.33 am Finish am 5 Start am Finish am 6 Start 8.09 am Finish 10.37am 7 Start 2.53 pm Finish 6.30 pm 8 Start 6.39 am Finish am 9 Start 2.15 pm Finish 5.47 pm 10 Start 3.12 pm Finish 8.01 pm 11 Start 0900 Finish Start 1117 Finish Start 1531 Finish Start 1652 Finish Start 2034 Finish Start 1615 Finish Start 1741 Finish Start 2359 Finish Start 1742 Finish Start 1936 Finish 2233 S2 Level 3/4 Course -23- Maths Department

24 Exercise 2 (C) Find the times taken for each of the following journeys 1 Start 9.23 pm Finish 3.17 am 2 Start 7.24 pm. Finish 6.18 am 3 Start pm Finish 5.17 am 4 Start 1537 Finish Start 1927 Finish Start 1736 Finish Jamie goes to bed at 1034 pm and wakes up the next morning at 7.16 am. How long is he asleep? 8 Mr Thomson decides to drive overnight from Glasgow to London to avoid traffic jams. He sets off at pm and arrives in London at 5.17 am. How long did his journey take? 9 The trans-siberian railway runs from Moscow to Vladivostok. A train leaves Moscow at 10 am on Monday and arrives at Vladivostock at 3 pm the following Monday. How long does the journey take? Exercise 3 (A) 1 How far does a car go in 3 hours at a speed of 50 mph? 2 How far does a bus go in 4 hours at a speed of 40 mph? 3 How far does an aeroplane fly in 6 hours at a speed of 350 mph? 4 How far can you cycle in 3 seconds at a constant speed of 7 m/s? 5 An express train is going at a constant speed of 60 m/s. How far does it go in 8 seconds? 6 A jet plane is flying at a constant speed of 250 m/s. How far does it go in 3 seconds? 7 If you go at a speed of 4 m/s, how far do you go in 10 seconds? 8 An ambulance travels at 70 mph for 3 hours. How far does it travel in that time? Maths Department -24- S2 Level 3/4 Course

25 9 A veteran car travels at 15 mph for 5 hours. How far does it travel? 10 Find the distance travelled in 3 hours at an average speed of 55 km/h. 11 Find the distance travelled in 5 hours at an average speed of 44 mph. 12 Find the distance travelled in 30 seconds at an average speed of 8 m/s. 13 Find the distance travelled in 7 5 hours at an average speed of 80 km/h. 14 Find the distance travelled in 12 hours at an average speed of 30 mph. Exercise 3 (B) 1 An aircraft travels at a steady speed of 600 km/h for 4½ hours. How far does it travel? 2 A model speedboat travels at 2.5 m/s for 16 seconds. How far does it travel? 3 A mole burrows through the earth at a speed of 18 cm per minute. How far will it burrow in 15 minutes? 4 Calculate the distance travelled at 30 km/h for 5 hours. 5 Calculate the distance travelled at 15 km/h for 7 hours. 6 Calculate the distance travelled at 70 km/h for 3 hours. 7 Calculate the distance travelled at 40 km/h for 4 hours 30 minutes. 8 Calculate the distance travelled at 25 km/h for 6 hours 30 minutes. 9 Calculate the distance travelled at 75 km/h for 30 minutes. 10 Calculate the distance travelled at 38 km/h for 3 hours 30 minutes. 11 Calculate the distance travelled at 24 km/h for 1 hour 15 minutes. 12 Calculate the distance travelled at 59 km/h for 6 hours 45 minutes. 13 Calculate the distance travelled at 23 km/h for 5 hours 45 minutes. 14 Joseph drives from 5 pm until 8 pm at an average speed of 50 mph. How far does he drive? 15 Find the distance travelled in 2 hours 30 minutes at an average speed of 70 km/h. S2 Level 3/4 Course -25- Maths Department

26 16 Find the distance travelled in 3 hours 15 minutes at an average speed of 52 km/h. 17 Find the distance travelled in 6 hours 45 minutes at an average speed of 88 mph. 18 Mohammed drives from 6.50 pm until 9.05 pm at an average speed of 64 km/h. What distance does he travel? 19 Janet drives for 45 minutes at an average speed of 40 mph. Calculate the distance she travels. Exercise 3 (C) 1 Calculate the distance travelled at 14 km/h for 2 hours 6 minutes. 2 Calculate the distance travelled at 90 km/h for 8 hours 12 minutes. 3 Calculate the distance travelled at 150 km/h for 2 hours 18 minutes. 4 Calculate the distance travelled at 80 km/h for 4 hours 24 minutes. 5 Calculate the distance travelled at 60 km/h for 5 hours 25 minutes. 6 Calculate the distance travelled at 28 km/h for 7 hours 35 minutes. 7 Calculate the distance travelled at 56 km/h for 4 hours 36 minutes. 8 Calculate the distance travelled at 42 km/h for 4 hours 20 minutes. 9 Calculate the distance travelled at 90 km/h for 3 hours 29 minutes. 10 Calculate the distance travelled at 150 km/h for 2 hours 40 minutes. 11 Calculate the distance travelled at 120 km/h for 1 hour 40 minutes. 12 Benjamin travels overnight by train. The departure time is 2150 hours and the train travels at an average speed of 108 km/h, arriving at its destination at 0320 hours. What distance did Benjamin travel? 13 Zander drives from Aberdeen to Inverness at an average speed of 64 km/h. He leaves Aberdeen at 9.50 am and arrives in Inverness at pm. What distance is it from Aberdeen to Inverness? 14 Find the distance travelled in 39 minutes at an average speed of 60 mph. Maths Department -26- S2 Level 3/4 Course

27 15 Find the distance travelled in 1 hour 51 minutes at an average speed of 40 mph. 16 Find the distance travelled in 2 hours 18 minutes at an average speed of 30 mph. 17 Find the distance travelled in 1 hour 24 minutes at an average speed of 75 km/h. 18 Isla drives for 3 hours 30 minutes at an average speed of 70 mph on the motorway. Then she drives for 2 hours 15 minutes at an average speed of 40 mph on minor roads. How far did she travel altogether? Exercise 4 (A) 1 Pam cycled 20 metres in 4 seconds. What is her speed in m/s? 2 Ken is running at a constant speed. He covers 18 metres in 3 seconds. What is his speed? 3 A plane flying at a constant speed takes 5 seconds to go 1500 metres. What is its speed in m/s? 4 A lorry travelling along a motorway at a constant speed goes 100 metres in 4 seconds. What is its speed in m/s? 5 Find the average speed of a jogger who runs 18 miles in 3 hours. 6 Find the average speed of a train travelling 520 kilometres in 4 hours. 7 Find the average speed of a car covering 280 kilometres in 5 hours. 8 Find the average speed of Cheryl who walks 15 kilometres in 5 hours. 9 Find the average speed of an aeroplane which flies 2703 km in 3 hours. 10 Find the average speed of a space shuttle which flies miles in 12 hours. Exercise 4 (B) 1 Jill cycled 54 kilometres in 6 hours. What is her speed in km/h? 2 Calculate the average speed to travel 80 km in 20 hours. S2 Level 3/4 Course -27- Maths Department

28 3 Calculate the average speed to travel 72 km in 6 hours. 4 Calculate the average speed to travel 85 km in 17 hours. 5 Calculate the average speed to travel 121 km in 5 hours 30 minutes. 6 Calculate the average speed to travel 81 km in 2 hours 15 minutes. 7 Calculate the average speed to travel 324 km in 6 hours 45 minutes. 8 There used to be a train called the 'Cheltenham Flyer'. It went 120 miles from Cheltenham to London in 2 hours. What was its average speed? 9 It is 150 miles from Hereford to London by rail. The first train in the morning takes 3 hours for the journey. What is its average speed? 10 Penznace is 305 miles from London by rail. A train leaves Penzance at 5.18 am and gets to London at am. a How many hours does the journey take? b What is the average speed of the train? 11 From Carlisle to London is 300 miles. The 8.35 am train from Carlisle gets to London at pm. a How many hours does the journey take? b What is the average speed of the train? 12 An overnight train leaves London at 8 pm. It arrives at Dundee at 5 am the next morning. a How long does the journey take? b The distance from London to Dundee is 450 miles. What is the train's average speed for the journey? 13 In the year 1830 the mail coach from London to Edinburgh covered 400 miles in 40 hours. What was its average speed? 14 Sally takes 2 hours to cycle a distance of 18 miles. Calculate her average speed in mph. 15 Bruce takes 2½ hours to cycle a distance of 20 miles. Calculate his average speed in mph. Maths Department -28- S2 Level 3/4 Course

29 16 The distance by sea from Harwich to the Hook of Holland is 121 miles. The crossing by ferry takes to the nearest mph. hours. Calculate the average speed of the ferry, 17 Calculate the average speed of a coach which travels from Exeter to Manchester, a distance of 235 miles, in hours. 18 Calculate the average speed of a coach which takes 4¼ hours to travel from Carlisle to Birmingham, a distance of 196 miles. 19 A coach driver sets off at midday, and arrives at her destination, 275 miles away, at 5 pm. What was her average speed? 20 A cyclist starts off at 1 o'clock in the afternoon. He arrives at his destination, 63 km away, at 4 pm. Calculate his average speed. 21 An athlete is declared the fastest man in the world after running 100 metres in 9.77 seconds. Find his average speed in metres per second, correct to 2 decimal places. 22 The cheetah is the fastest land animal in the world. One cheetah was timed running 760 metres in 24 seconds. Find his average speed in metres per second, correct to 2 decimal places. 23 Find the average speed for each of these journeys: a Jensen drives 200 miles in 2 hours 30 minutes. b Lance cycles 135 miles in 3 hours 45 minutes. c Paula runs 40 5 kilometres in 2 hours 15 minutes. 24 Noelle drives to work each morning. The journey is 36 kilometres and it takes her 45 minutes to get there. Find her average speed. Exercise 4 (C) 1 Work out the average speeds of these trains. a London to Bristol, 118 miles in 1 hour 27 minutes. b London to Nottingham, miles in 2 hours 12 minutes. c London to Brighton (fast), 50 5 miles in 58 minutes. d London to Brighton (slow), 50 5 miles in 1 hour 12 minutes. S2 Level 3/4 Course -29- Maths Department

30 2 A train leaves London for Swansea at 9.15 am. It arrives in Swansea at am. a How long does the journey take, in hours and minutes? b The distance from London to Swansea is 191 miles. Work out the train's average speed. 3 This table shows main-line trains of several countries. Work out the average speed of each train, in km/h. Journey Distance (km) leaves arrives Calais - Paris pm 6.27 pm Dublin - Cork am am Zurich - Geneva am pm Rome - Milan pm pm Madrid - Barcelona pm pm Munich - Hamburg pm pm London - Edinburgh am 2.37 pm Moscow - Vladivostok am Monday 3 pm the following Monday 4 Find the average speed for the following journeys: a A bus travels 48 miles in 2 hours 24 minutes. b A car travels 124 kilometres in 3 hours 6 minutes. 5 Edith leaves home in her car at 7.45 am. She drives 90 miles to a meeting. If she arrives at 9.30 am, what was her average speed for the journey? (give your answer to the nearest kilometre per hour) 6 Lorenzo takes the 0730 train from Rome to Milan. The distance is 630 kilometres. If the train arrives in Milan at 1100 hours find its average speed. 7 In 2002, Steve Fossett became the first person to fly around the world non-stop in a balloon. He travelled kilometres in 14 days 20 hours. Find his average speed to the nearest kilometre per hour. Maths Department -30- S2 Level 3/4 Course

31 Exercise 5 (A) 1 Calculate the time taken to go 80 kilometres at a speed of 20 km/h. 2 Calculate the time taken to go 500 miles at a speed of 125 mph. 3 Calculate the time taken to go 432 metres at a speed of 8 m/s. 4 Calculate the time taken to go 630 kilometres at a speed of 90 km/h. 5 Calculate the time taken to go 504 kilometres at a speed of 72 km/h. 6 Calculate the time taken to go 448 miles at a speed of 56 mph. 7 Calculate the time taken to go 648 kilometres at a speed of 108 km/h. 8 Calculate the time taken to go 294 kilometres at a speed of 42 km/h. 9 Calculate the time taken to go 630 centimetres at a speed of 18 cm/s. 10 Calculate the time taken to go 100 metres at a speed of 10 m/s. 11 How many hours does it take to go 705 miles at 47 mph? 12 A motor boat has a speed of 4 mph. How many hours does it take to go 24 miles from Lulworth to Bournemouth? 13 A motor boat has a speed of 8 mph. How many hours does it take to go 32 miles from Swanage to Ventnor? 14 A motor boat has a speed of 5 mph. How many hours does it take to go 60 miles round the Isle of Wight? 15 Calculate the time taken for each of the following journeys: a 210 km at an average speed of 70 km/h. b 160 m at an average speed of 8 m/s. c 175 miles at an average speed of 35 mph. d 78 cm at an average speed of 3 cm/s. e 1360 km at average speed of 160 km/h. S2 Level 3/4 Course -31- Maths Department

32 Exercise 5 (B) 1 Calculate the time taken (in hours and minutes) to go 150 miles at an average speed of 60 mph. 2 Calculate the time taken (in hours and minutes) to go 44 km at an average speed of 16 km/h. 3 Calculate the time taken (in hours and minutes) to go 350 km at an average speed of 56 km/h. 4 Sasha drives 180 miles at an average speed of 40 mph. How long will her journey take her? 5 Calculate the time taken for each of the following journeys: a 90 km at an average speed of 20 km/h. b 420 miles at an average speed of 120 mph. c 432 m at an average speed of 8 m/s. d 585 km at an average speed of 90 km/h. e 306 km at average speed of 72 km/h. f 322 miles at an average speed of 56 mph. g 351 km at an average speed of 108 km/h. h 630 km at an average speed of 42 km/h. i j 315 cm at an average speed of 18 cm/s. 125 m at average speed of 10 m/s. Exercise 5 (C) 1 Calculate the time taken (in hours and minutes where necessary) for the following journeys. a 100 km at 4 km/h c 21 km at 6 km/h b 60 km at 10 km/h d 45 km at 10 km/h e 36 km at 30 km/h f 70 km at 40 km/h g 240 km at 36 km/h h 9 1 km at 17 km/h Maths Department -32- S2 Level 3/4 Course

33 2 A plane travels at 240 km/hr. How long will it take to travel 840 km. (Answer in hours and minutes) 3 A car travels 320 km at 48 km/hr. If it starts its journey at 0852 a how long will the trip take? b at what time will it finish its trip? 4 Change these to hours and minutes, to the nearest minute. a 2 5 hours c 3 03 hours b 5 72 hours d hours 5 a Calculate the time taken, in hours, to travel a distance of 115 miles at a speed of 35 mph. Give the answer to 2 decimal places. b Change the answer to (a) into hours and minutes. 6 Find the time taken to do these journeys. Give each time in hours and minutes, to the nearest minute. a 145 miles at 55 mph c 65 miles at 90 mph b 385 miles at 125 mph d 48 miles at 110 mph 7 A light aircraft sets out on a journey of 685 miles. It travels at a speed of 155 mph. a Calculate the journey time in hours and minutes. b If the aircraft sets out at 6.30 am, at what time will it finish the journey? 8 A motorboat travels at a speed of 18 mph. The boat sets out on a journey of 49 miles. a How long will the journey take, in hours and minutes? b If the boat starts out at 3.15 pm, at what time will it finish the journey? 9 A damaged ship is drifting at a speed of 3 5 mph towards some rocks. At 2.45 pm the ship is 18 7 miles from the rocks. a How long will it take, in hours and minutes, for the ship to reach the rocks? b At what time will it reach the rocks? S2 Level 3/4 Course -33- Maths Department

34 10 A steamer on a loch travels from the northern end of the loch to the southern end at a speed of 13 mph. The distance from the northern end to the southern end is 63 miles. If the steamer leaves the northern end at 2.30 pm, at what time will it arrive at the southern end? 11 Change these into hours, correct to 2 decimal places. a 4 hours 16 minutes c 8 hours 50 minutes b 3 hours 7 minutes d 4 hours 47 minutes e 13 minutes f 28 minutes 12 A train travels a distance of 64 miles in 1 hour 23 minutes. Calculate the train's average speed, to the nearest mph. 13 Calculate the average speed of each of these, to the nearest mph. a A car which travels 72 miles in 1 hour 42 minutes. b A bicycle which travels 19 miles in 2 hours 9 minutes. c An athlete who runs 23 miles in 3 hours 37 minutes. 14 A coach leaves London at 5.15 pm and arrives at Bristol at 7.50 pm. The distance from London to Bristol is 119 miles. a How long does the coach take to travel from London to Bristol, in hours and minutes? b Calculate the average speed of the coach, to the nearest mph. 15 a A train leaves Glasgow at It travels the 400 km to Manchester at 64 km/h. When did it arrive in Manchester? b It stayed in the station for 80 minutes. When did it leave? c It returned to Glasgow 45 minutes quicker than the first part of the trip. When did it arrive back in Glasgow? How long did it take? d What was the speed of the train on the return trip? e A second train, also made the return trip but left 1 hour later and travelled at half the speed of the first train. When did it arrive? 16 How long did it take for a speedboat to go from Hastings to Cherbourg, given that the two towns are 195 km apart and that the speedboat recorded an average speed of 60 km/h? Maths Department -34- S2 Level 3/4 Course

35 17 Jan set out for work at 7.50 am and drove 18 miles to her office at an average speed of 24 mph. When did she arrive at the office? 18 Steve takes the train from Birmingham to London, a distance of 180 km. If the train set out at 0904 hours and travels at an average speed of 72 km/h, when does Steve arrive in London? 19 Calculate the time taken for each of the following journeys. a 228 km at 60 km/h c 94 km at 40 km/h b 99 miles at 30 mph d 120 km at 90 km/h. 20 The distance from Inverness to London is 552 miles. Richard takes the 2020 train from Inverness to London. This train travels at an average speed of 60 mph. When will Richard arrive in London? 21 Mary drives 24 miles from Glasgow to Gourock. Her average speed is 48 mph. She then waits 15 minutes before taking the ferry from Gourock to Dunoon. The crossing is exactly 3 miles and the average speed of the ferry is 10 mph. How long did it take Mary to get from Glasgow to Dunoon? 22 Tony must reach the airport by 1510 hours in order to book in for a flight. He plans to travel the 35 miles from his home to the airport by minibus. The minibus can only do this journey at an average speed of 28 mph. What is the latest time that Tony can leave his home? Exercise 6 (B) 1 Find the average speed for each of these journeys. a Shaun drives 245 miles in 7 hours b An aircraft flies 1125 kilometres in 1 hour 15 minutes c Sarah drives 171 kilometres in 4 hours 45 minutes. 2 Calculate the time taken (in hours and minutes) for each of the following journeys. a 132 km at an average speed of 12 km/h b 351 miles at an average speed of 52 mph S2 Level 3/4 Course -35- Maths Department

36 c 95 km at an average speed of 38 km/h. 3 Calculate the distance travelled in journeys whose times and average speeds are: a 4 hours, 69 mph b 3 hours 15 minutes, 64 km/h c 5 hours 30 minutes, 92 km/h. 4 A and B are two aircraft. Aircraft A flies a distance of 962 miles in 2 hours. Aircraft B flies a distance of 1644 miles in 3 5 hours. Calculate the average speed of each aircraft, and say which one flew faster, on average. 5 A freight train travels at a steady speed of 35 mph. a Calculate the time taken, in hours, to travel a distance of 168 miles. Give the answer in decimals. b Change your answer to hours and minutes. 6 At a constant speed of 13 m/s, how far will a racing bike go in a 10 seconds b 1 minute? 7 A woman goes on a country walk. She covers 18 miles in 4 hours, at a steady speed. What is her speed in miles per hour? 8 A train's average speed for a 450 mile journey is 90 mph. How long does the journey take? 9 A coach starts from Bournemouth at 7.30 am and arrives in York at 2.30 pm. a How long does the journey take? b From Bournemouth to York is 252 miles. What is the average speed of the coach? Maths Department -36- S2 Level 3/4 Course

37 Exercise 6 (C) 1 It takes 1¼ hours to serve dinner on board a jet plane. The plane is travelling at 520 mph. How far does it travel while dinner is being served? 2 This diagram shows the timetable of a train from Edinburgh to King's Cross. The numbers in boxes are distances between the stations, in miles. a How long does the train take to travel from Edinburgh to Dunbar? Give your answer in minutes. b Change your answer to part (a) into a decimal of an hour. c Calculate the average speed of the train between Edinburgh and Dunbar, to the nearest mph. d Calculate the average speed of the train, to the nearest mph, between i Dunbar and Newcastle ii Newcastle and Darlington iii Darlington and Doncaster iv Doncaster and King's Cross. 3 a A car travels for 3 hours at 62 km/h. How far did it travel? b If it increases its speed by 10 km/h for the next 2 hours, calculate the distance it travels during this period. c Calculate the total distance travelled. 4 Khalid has to drive 211 miles on the motorway. He reckons he can average 60 mph. He enters the motorway at a quarter past 10. What time does he expect to leave the motorway? 5 A high-speed train travels between two stations at a constant speed of 125 mph. The stations are 25 miles apart. How many minutes does it take to go that distance? S2 Level 3/4 Course -37- Maths Department

38 6 Two old cars have a race from London to Brighton, a distance of 60 miles. The winner does the journey at an average speed of 24 mph. The loser gets to Brighton 1½ hours after the winner. What is the average speed of the loser? 7 The space-shuttle travels at mph. a How far does it travel in 1 day? b How long does it take to travel 1 million miles? Give your answer in days and hours. 8 The 1045 train leaving London is due at Preston at 1315, at Carlisle at 1420 and at Glasgow at At Preston this train is 17 minutes late. By Carlisle it has made up 10 minutes. a Write down the actual arrival times of the train at Preston and Carlisle. b At what average speed would the train have to travel from Carlisle to Glasgow, a distance of 156 km, to arrive on time? 9 Camilla leaves London at 8.55 am to drive to Truro in Cornwall, a distance of 450 kilometres. If she averages a speed of 60 km/h, when will she arrive in Truro? 10 A high speed train travels from Hamburg to Munich in Germany. The train leaves at 2215 hours and travels at an average speed of 140 km/h. If the train arrives in Hamburg at 0400 hours the following morning, find the distance it travels. 11 William drives coaches. One morning he drove from 9.50 am until am without stopping. When he checked his trip counter, he discovered that he had travelled 112 miles. Calculate his average speed for the drive. Maths Department -38- S2 Level 3/4 Course