# Time & Distance SAKSHI If an object travels the same distance (D) with two different speeds S 1 taking different times t 1

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1 Time & isance The raio beween disance () ravelled by an objec and he ime () aken by ha o ravel he disance is called he speed (S) of he objec. S = = S = Generally if he disance () is measured in kilomeers (KM), he ime () will be measured in hours (h) or if he disance () is measured in meers (m), hen he ime () will be measured in seconds (s). Speed (S)= KM m = = KMPH (OR) = mps H s i.e. he speed will be measured in KMPH or mps. 1KM 1000m KMPH = = = mps 1mps = KMPH 1H 3600Secs 8 5 If an objec ravels he same disance () wih wo differen speeds S 1 and S 2 aking differen imes 1 and 2 hen S 1 :S 2 = : = 2 : 1 1 : 2 = S 2 :S 1 FORMULAE i) Two objecs ravel he same disance () wih differen spee ds of S 1 and S 2. If he difference beween he journey imes is hen 1 1 (S S ) = S1 S 2 2 S ii) If an objec ravels a disance of wih a speed of S 1 and reurns wih a speed of S 2 aking a oal ime of '', hen SS 1 2 = S1+ S2 iii) If wo objecs ravel he same disance wih speeds of S 1 and S 2 aking he journey imes of 1 and 2 respecively, hen S 1 :S 2 = 2 : 1 OR 1 : 2 = S 2 :S 1

2 iv) Walking a p/q h of usual speed a man reaches his desinaion -hours lae (or early) hen usual ime o reach he office is given by p p q v)if a person walks a disance wih a speed of S 1 kmph hen he will be lae (early) by 1 hours. If he walks a S 2 kmph he will be lae (early) by 2 hours. Then he disance ravelled by he person is Noe: Use (+) sign if he person is lae in one case and early in he oher case. Use (-) sign if he is lae in boh he cases or early in boh he cases. vi) If an objec ravels differen disances wih differen speeds during a journey hen he enire journey can be represened by a single equivalen speed called Average Speed (S A ) Toal is an ce(t.) Average Speed (S A ) = ToalTime(T.) vii) If an objec ravels a disance of 1 km wih S 1 kmph anoher 2 km wih a speed of S 2 -kmph and 3 -km wih a speed of S 3 -kmph, hen he average speed of he journey is S A S S 1 2 = 1± 2 S1 S 2 ( ) = S1 S2 S3 viii) If an objec ravels wih a speed of S 1 -kmph for 1 -hours, nex wi-h a speed of S 2 kmph for 2 -hours and wih a speed of S 3 -kmph for 3 hours, hen he average speed (S A ) for he whole journey is (S11 + S22 + S3 3) SA = ( + + ) PROBLEMS 1. A bus covers a disance of 624 km in 780 minues. Wha is he average speed of he bus in kmph? 1) 44 2) 48 3) 4) Canno be deermined 5) None of hese 624 S = = = 48 kmph Soluion: = 624 km = 780 min = 13 h 13

3 2. The average speed of a bus is 55 kmph. How much disance will a car cover in eigh hours if he average speed of he car is 26 percen more han he average speed of he bus? 1) km 2) km 3) km 4) km 5) None of hese Ans: 4 Soluion: S b = 55 kmph, S c = = 69.3, = 8 h 100 =S = = km 3. One hird of a cerain journey is covered a he rae of 25km/hour, one-fourh a he rae of 30 km/ hour and he res of 50 km/hour. The average speed for he whole journey is? 1) 35 km/hour 2) 33 1 /3 km/hour 3) 30 km/hour 4) 37 1 / 12 km/hour 5) None of hese Soluion: Le he oal disance covered = 600 km isance covered wih he speed of 25 km/hr = 200 km isance covered wih he speed of 30 km/hr = 150 km isance covered wih he speed of 50 km/hr = 250 km Toal ime aken o cover he disance = Average speed = 8+5+5=18 h = = km/hr 4. A car covers a disance from o-wn A o own B a he speed of 58 kmph and covers he disance fr-om own B o own A a he speed of kmph. Wha is he appro-ximae average speed of he car? 1) 55 kmph 2) kmph 3) 48 kmph 4) 50 kmph 5) 60 kmph Ans: 1 Soluion: isance beween AB be 58 Toal disance covered = 2 58 Time aken by car o ravel from 58 A o B = = 58 Time aken by car o ravel from

4 58 B o A = 58 Toal ime = + 58 = 110 Average speed 2 58 = 55kmph The average speed of a rain is 1 3 / 7 imes he average speed of a car. The car covers a disance of 588 km in 6 hours. How much disance will he rain cover in 13 hours? 1) 1750 km 2) 1760 km 3) 1720 km 4) 1850 km 5) None of hese Ans: 5 Soluion: Speed of car = = 98 Speed of rain = = 140 kmph isance covered by he rain = = 1820 km 6. A person leaves a place A o pla-ce B a 6 a.m. and reaches place B a 10 a.m. Anoher person leaves B a 7:30 a.m. and reaches A a 11 a.m. They will mee each oher a? 1) 7:40 a.m. 2) 8:20 a.m. 3) 8:40 a.m. 4) 9:20 a.m. 5) None of hese Ans: 3 Soluion: Le disance be 28 km 28 Speed of he firs person = = 7 4 Speed of he second person 28 = = isance covered by he firs person upo 7:30 a.m. = = 10.5 Remaining disance = = 17.5 km Time aken by boh he persons o ravel 17.5 km = = 1 hr 10 min Time hey me = 7: hr 10 min = 8:40 a.m.

5 7. If a man decides o ravel 80 km in 8 hours, parly by foo and parly on, a bicycle, his speed on foo being 8km/hr and ha on bicycle being 16 km/hr, wha disance would he ravel on foo? 1) 20 km 2) 48 km 3) 36 km 4) 40 km 5) None of hese Soluion: Le he ime aken o ravel a par of disance by foo = x Time aken o ravel by bicycle = 8 x 8 x + 16 (8 x ) = 80 8x x = x = 48 x = = 6 8 isance ravelled by foo = 8 6 =48 km 8. A car covers he firs 39 km of is journey in 45 minues and he remaining 25 km in 35 minues. Wha is he average speed of he car? 1) 46 km/hr 2) 40 km/hr 3) 48 km/hr 4) 42 km/hr 5) None of hese Ans: 3 Soluion:Toal disance = = 64 km Toal ime = = 80 min = 4/3 hr Average speed = = = 16 3 = 48 km/hr 9. A man walks a cerain disance and rides back aking a oal ime of 37 minues. He could walk boh ways in 55 minues. How long would he ake o ride boh ways? 1) 19 minues 2) 20 minues 3) 9.5 minues 4) 18 minues 5) None of hese Ans: 1 Soluion: Walk + ride = 37 min 2 Walk = 55 W = 27.5 Ride = = 9.5 Ride boh ways = = 19 min 10. Walking 6/7 h of his usual speed, a man is 12 minues oo lae. The usual ime aken by him o cover ha disance is? 1) 1 hour 2) 1 hour 12 minues 3) 1 hour 15 minues 4) 1 hour 20 minues 5) None of hese

6 p 6 Soluion: Refer o formula (iv) =, = 12 q 7 Usual ime 6 12 = = 72 = 1 hr 12 min If I walk a 5 km/hour, I miss a rain by 7 minues. If, however, I walk a 6 km/hour, I reach he saion 5 minues before he deparure of he rain. The disance (in km) beween my house and he saion is? 1) 6 km 2) 5 km 3) 4 km 4) 3 km 5) None of hese Ans: 1 Soluion:Refer o formula (v) S 1 = 5, S 2 = 6, 1 = 7 min, 2 = 5 min isance beween my house and Saion 5 6 (7 + 5) = = = 6km A walks a a uniform rae of 4 km an hour and 4 hours afer his sar, B bicycles afer him a he uniform rae of 10 km an hour. How far from he saring poin will B cach A? 1) 16.7 km 2) 18.6 km 3) 21.5 km 4) 26.7 km 5) None of hese Ans: 4 Soluion:isance covered by A in 4 hours = 16 km For every hour B covers 6 km more han A. So he covers 16 km in 16 8 = hours isance covered by B in hours is 10 = 3 3 = 26.7 km 13. If a man walks 20 km a 5 km/hr, he will be lae by 40 minues. If he walks a 8km per hr, how ear-ly from he fixed ime will he re-ach? 1) 15 minues 2) 25 minues 3) 50 minues 4) 1½ minues 5) None of hese Ans: 3 Soluion: Refer o formula (v) = 20 km, S 1 = 5, S 2 = 8, 1 = 40 min, 2 =? 5 8 (40 2) 2(40 2) 20 = + = = 90 2 = 50 minues The man reaches 50 minues early from he fixed ime.

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