GOING MY WAY EXAMPLES

Transcription

1 GOING MY WAY EXAMPLES When an object moves at a constant speed, or rate, it is said to be in uniform motion. The formula d = rt is used to solve uniform motion problems. In the formula, d represents distance, r represents rate, and t represents time. In the formula, r can represent an average rate instead of a constant rate. Example # 1 Joe rides his bicycle at a speed of 8 mph (miles per hour). How long will it take him to ride 28 miles? Explore Let t = the time it takes Joe to ride 28 miles. 28 = 8t Solve d = rt 28 = 8t = t Joe will take hours to ride 28 miles. Examine 28 = (3 2 1 )(8) 28 = 28

2 Discussion question # 1 If Sue doubles her speed and doubles the distance traveled, what effect does this have on the time needed? (Remains the same) Example # 2 Doug and Wanda leave their home in Chattanooga at the same time. They travel in opposite directions. Doug travels at 80 km/h (kilometers per hour) and Wanda travels 72 kh/h. In how many hours will they be 760 km apart? Doug 760 km Wanda 80 km/k 72 km/k Explore Let t = represent the number of hours. Plan r(t) = d Doug 80 t 80t Wanda 72 t 72t They travel a total of 760 km. Doug s distance + Wanda s distance = total distance 80t + 72t = 760 Doug travels 80t km. Wanda travels 72t km. Solve 80t + 72t = t = 760 t = 5 In 5 hours, Doug and Wanda will be 760 km apart. Examine 80(5) + 72(5) = = = 760

3 Example # 3 Suppose Dan and Donna leave at the same time traveling the same direction. Dan drives 70 km/h, Donna drives 85 km/h. How long until they are 90 km apart? Donna D 1 = 85(t) Dan D 2 = 70(t) 90 km Explore Let t = represent the number of hours. Plan 85t 70t = 90 Dan 70 t 70t Donna 85 t 85t Doug travels 70t km. Wanda travels 85t km. The distance between what Donna drives and what Dan drives is 90 km. Donna s distance Doug s distance = 90 km. 85t 70t = 90 Solve 85t 70t = 90 15t = 90 t = 6 In 6 hours, Donna and Dan will be 90 km apart. Examine 85(6) 70(6) = = = 90

4 Example # 4 At 8:00 A.M. Peggy leaves home driving 35 mph. A half hour later, Doug discovers that she left her briefcase. He drives 50 mph to catch up with her. If Doug is delayed 15 minutes with a flat tire, at what time will he catch up to Peggy? Explore Let x = the time Peggy travels until Doug arrives. Plan r(t) = d Peggy 35 x 35x Doug 50 3 x (x - ) 4 Peggy travels 35x mi. Doug travels (50x 37.5 mi. Peggy and Doug travel the same distance. 35x = 50x 37.5 Solve 35x = 50x x = x = 2.5 Peggy has been traveling for hours when Doug catches up to her. Doug catches up to Peggy at 8 A.M hours or 10:30 A.M. Examine 35(2.5) = 50(2.5) = = 87.5

5 Name: Date: Class: GOING MY WAY WORKSHEET Use the 4-step approach to problem solving: 1. Explore Define a variable 2. Plan Write an equation 3. Solve Solve the equation and answer the problem 4. Examine Check to see if the answer makes sense 1. Pat is driving 80 km/h. How far will she travel in 2 hours? 2. Marilyn traveled 240 miles. What was her rate if she made the trip in 6 hours? 3. Rudy rode his bicycle 72 km. How long did it take him if his rate was 9 km/h? 4. Two trains lave Bridgeport at the same time, one traveling north, the other south. The first train travels at 40 mph and the second at 30 mph. In how many hours will the trains be 245 miles apart? 5. Two cyclists are traveling in the same direction on the same course. One travels 20 mph and the other 14 mph. After how many hours will they be 15 miles apart? 6. An express train travels 80 km/h from Wheaton to Whitfield. A passenger train, traveling 48 kh/h, takes 2 hours longer for the same trip. If the time for the express train is x hours, how far apart are Wheaton and Whitfield? 7. At 1:30 P.M., a plane leaves Tucson for Baltimore, a distance of 2240 miles. The plane flies 280 mph. A second plane leaves Tucson at 2:15 P.M., and is scheduled to land in Baltimore 15 minutes before the first plane. At what rate must the second plane travel to arrive on schedule?

6 GOING MY WAY WORKSHEET KEY Use the 4-step approach to problem solving: a. Explore Define a variable b. Plan Write an equation c. Solve Solve the equation and answer the problem d. Examine Check to see if the answer makes sense 1. Pat is driving 80 km/h. How far will she travel in 2 hours? Explore Let d = distance Pat can travel in 2 hours. d = (80)(2) Solve d = rt d = (80)(2) d = 160 Pat will travel 160 km in 2 hours. Examine 160 = (80)(2) 160 = 160

7 2. Marilyn traveled 240 miles. What was her rate if she made the trip in 6 hours? Explore Let r = rate Marilyn travels. 240 = r(6) Solve d = rt 240 = 6r 40 = r Marilyn will travel 40 mph. Examine 240 = 40(6) 240 = Rudy rode his bicycle 72 km. how long did it take him if his rate was 9 km/h? Explore Let t = time is too Rudy to ride 72 km. 72 = 9(t) Solve d = rt 72 = 9t 8 = t It will take Rudy 8 hours to go 72 km. Examine 72 = 9(8) 72 = 72

8 4. Two trains lave Bridgeport at the same time, one traveling north, the other south. The first train travels at 40 mph and the second at 30 mph. In how many hours will the trains be 245 miles apart? Explore Let t = time the two trains were traveling. d 1 = (40)t d 2 = (30)t The total distance the train covered is 245 miles. d 1 + d 2 = Total distance 40t + 30t = 245 Solve 40t + 30t = t = 245 t = 3.5 In hours the two trains will be 245 miles apart. 1 Examine 70( 3 ) = = 245

9 5. Two cyclists are traveling in the same direction on the same course. One travels 20 mph and the other 14 mph. After how many hours will they be 15 miles apart? Explore Let t = time the two cyclists were on the road. d 1 = (20)t d 2 = (14)t The difference between the two cyclists is 15 miles. d 1 - d 2 = distance apart 20t 14t = 15 Solve 20t 14t = 15 6t = 15 t = 2.5 In hours the first cyclist will lead the second cyclist by 15 miles. Examine 20(2.5) 14(2.5) = = = 15

10 8. An express train travels 80 km/h from Wheaton to Whitfield. A passenger train, traveling 48 kh/h, takes 2 hours longer for the same trip. If the time for the express train is x hours, how far apart are Wheaton and Whitfield? Explore Let x = time the express train is traveling. Let (x x + 2) = time passenger train is traveling. d 1 = (80)( x ) d 2 = (48)( x + 2) Distance both trains travel are equal. d 1 = d 2 80 x = 48( x + 2) Solve 80 x = 48( x + 2) 80 x = 48 x x = 96 x = 3 x = 9 It takes the express train 9 hours to make the trip. d = (80) 9 d = 240 km Examine 80( 9 ) = 48( 9 + 2) 240 = 48(5) 240 = 240

11 6. At 1:30 P.M., a plane leaves Tucson for Baltimore, a distance of 2240 miles. The plane flies 280 mph. A second plane leaves Tucson at 2:15 P.M., and is scheduled to land in Baltimore 15 minutes before the first plane. At what rate must the second plane travel to arrive on schedule? Let x = time first plane leaves Tucson. Second plane leaves 45 minutes later and lands 15 minutes earlier. Therefore, plane two is in the air 1 hour less (x 1). Plane = 280(x) Plane = r(x 1) Distances both planes travel are equal. Solve Plane = 280x x = 8 hours for plane 1 Plane = r(8 1) 2240 = 7r 320 = r Plane 2 travels 320 miles per hour. Examine 2240 = (320)(8 1) 2240 = (320)(7) 2240 = 2240

12 Student Name: Date: GOING MY WAY CHECKLIST 1. On each problem, did the student diagram and label problem correctly? a. All seven (30 points) b. Six of the seven (25 points) c. Five of the seven (20 points) d. Four of the seven (15 points) e. Three of the seven (10 points) f. Two of the seven (5 points) 2. On each problem, did the student use the 4-step approach to problem solving? a. All seven (30 points) b. Six of the seven (25 points) c. Five of the seven (20 points) d. Four of the seven (15 points) e. Three of the seven (10 points) f. Two of the seven (5 points) 3. On each problem, did the student solve the problem correctly? a. All seven (30 points) b. Six of the seven (25 points) c. Five of the seven (20 points) d. Four of the seven (15 points) e. Three of the seven (10 points) f. Two of the seven (5 points) Total Number of Points A B C D F 81 points and above 72 points and above 63 points and above 54 points and above 53 points and Any score below C needs remediation!