SPEED, DISTANCE Speed, distance problems can be solved with the following formula Speed = distance/time Let s take a typical example. A man went on a trip. His average speed was 60mph. If he traveled for four hours, how far did he go? Putting the known values into the formula we get 60 = X/4, where X represents the number of miles traveled. In order to get X alone we multiply both sides of the equation by 4. (4)(60) = (4)(X/4) 240 = X Therefore the man traveled 240 miles. Let s look at a similar example. There was a girl that ran at the speed of 200m/min. If she ran for 10 minutes, how far did she go. Putting the known values into the equation we get 200 = X/10, where X stands for the number of meters she ran. In order to get X alone we multiply both sides by 10. (10)(200) = (10)(X/10) 200 = X Therefore the girls ran 2000 meters.
Now, let s make the unknown variable the speed. In this example a lady went on a trip of 150km that took her 3 hours to complete. What was her average speed? Putting the known values into the equation we get X = 150/3, where X represents the speed. Dividing 150 by 3 we get X = 50. Therefore the lady averaged 50km/hour. Let s look at a similar example. A boy ran a 1600m race in 5 minutes. What was his average speed? Putting the known values into the equation we get X = 1600/5, where X represents the speed. Dividing 1600 by 5 we get X = 320. Therefore, the boy averaged 320m/minute. Now, let s make the unknown variable the time. In this example, a supertrain went 300 miles at 120mph. How long did it take? Putting the known values into the equation we get 120 = 300/X, where X represents the time. Our goal is to get X alone and out of the denominator so we multiply both sides of the equation by X. (120)(X) = (300/X)(X) results in 120X = 300. Next we divide both sides of the equation by 120. 120X/120 = 300/120 results in X = 2.5. Therefore, it took 2.5 hours.
Let s look at a similar example. A cyclist pedaled 33km at 11km/hour. How long did it take? Putting the known values into the equation we get 11 = 33/X, where X represents the time. Once again our goal is to get X out of the denominator and alone. To do this we multiply both sides of the equation by X. (11)(X) = (33/X)(X) results in 11X = 33 Next we divide both sides of the equation by 11. 11X/11 = 33/11 results in X = 3. Therefore it took 3 hours. Other speed-distance problems may appear to be more complicated, but in the end they are merely variations of this approach. Problems 1. A van traveled 216 km. in four hours. Find its average speed in km/h. 2. David swam 800 m. in 20 minutes. Find his average speed in m/min. 3. A car traveled at an average speed of 80 km/hr for five hours. What was the distanced traveled? 4. Jerome took 15 minutes to walk from his house to a community center. His average speed was 60 m/min. What is the distance from Jerome s house to the community center? 5. A train traveled 30 miles at an average speed of 60 mi/hr. Find the time taken for the trip. 6. A car traveled from Town A to Town B at an average speed of 80 KM/hr. How long did the trip take? 7. Shawn takes two minutes to cycle 800 meters.
A. What is his average speed? B. If he continues to cycle for another five minutes at the same average speed, how much further will he travel? 8. Tyler took two hours to drive from Town A to Town B which were 150 KM. apart A. What is his average speed? B. How many hours would he take to drive from Town B to Town A if the average speed for the return trip was 60 km/hr. 9. Miguel walked 910 m. from home to his office. His average speed was 70 m/min. He left home at 7:30AM. At what time did he arrive at the office? 10. Amanda took six minutes to walk from her school to the nearest train station. Her average speed was 80 m/min. How long would she take if her average speed was 60 m/min? 11. Meihua jogged for 1/2 hour at 6 km/hr. She jogged for another 1/4 hour at 8 km/hr. What distance did she jog altogether? 12. In a 9 km walkathon, Susan walked at an average speed of 6 km/hr. for the first 3 km. and at an average speed of 4 km/hr for the remaining distance. How much time did she take for the walkathon? 13. Ryan and David both cycled from Town X to Town Y. They started at the same time. After cycling for four hours, Ryan completed the trip, but David still had 2 km. to cycle. If Ryan s average speed was 10 km/hr, find David s average speed for four hours. 14. A car traveled from Town X to Town Y at an average speed of 88 km/hr. Then it traveled from Town Y to Town Z at an average speed of 64 km/hr. A. Find the total time. B. Find the average speed for the whole trip. 15. Ali cycled from Town A to Town B. He covered 1/5 of the trip in the first hour and 1/3 of the trip in the second hour. He took two hours to cycle the remaining 14 km. Find his average speed for the whole trip. 16. John and Peter traveled from Town P to Town Q. Peter left Town P at 8:30AM John left Town P one hour later. They both reached Town Q at 1:30PM If Peter s average speed for the trip was 60 km/hr, what was John s average speed? 17. Danny jogged at an average speed of 12 km/hr for 20 minutes. What distance did he jog? 18. At 2:20PM a van left Town A and traveled towards Town B at an average speed of 40 km/hr. At 2:30PM a car left Town B and traveled towards Town A along the same road at an average speed of 60 km/hr. The car arrived at Town A at 3:30pm. What time did the van arrive at Town B? 19. Mr. Bode takes four hours to complete a trip at an average speed of 60 km/hr. If he increases his average speed to 80 km/hr, how long will he take to complete the trip?
20. At 8:00AM Ryan left Town A and cycled towards Town B at 12 km/hr. At the same time Scott left Town B and cycled towards Town A at 16 km/hr along the same road. At 8:30AM they were still 4 km. apart. What is the distance between the two towns? 21. Jordon took three hours to travel from Town X to Town Y. His average speed was 50 km/hr. On his way back he took one hour less. What was the average speed on the return trip? 22. Mr. Miles drove a distance of 150 km. from Town A to Town B. His average speed was 60 km/hr. How much time would he save if he increased his average speed for the trip by 15 km/hr. 23. Mr. Rand took 20 minutes to travel from Town A to Town B. His average speed was 66 km/hr. What is the distance between the two towns? 24. Josh cycled from Town A to Town B. He took 3/4 of an hour to cycle 1/4 of the trip at 16km/hr. He cycled the remainder at 12 km/hr. He reached Town B at 10:30AM. What time did he leave Town A? 25. Jesse drove from Town A to Town B. At 8:30AM he had traveled 2/3 of the trip. He traveled the remainder of the trip at an average speed of 80 km/hr and reached Town B at 8:45AM. If his average speed for the whole trip was 90 km/hr, what time did he leave Town A? 26. John took four hours to cycle 3/5 of a trip. He took two hours to cycle the remaining 30 km. Find his average speed for the whole trip. 27. Tyrone took 1 1/2 hours to cover 2/3 of a trip. He took 1/2 hour to cover the remainder of the trip at an average speed of 72 km/hr. What is the average speed for the whole trip? 28. John and David both drove a distance of 80 km. from Town X to Town Y. John left Town X twenty minutes earlier than David. They reached Town Y at the same time. If John s average speed was 60 km/hr, what was David s average speed? 29. The train took 45 minutes to travel from Town A to Town B. The average speed for the trip was 80 km/hr. What was the distance between the two towns? 30. John is swims 50m in 40 seconds. What is his speed? 31. A ball rolled 450cm in 15 seconds. What is its average speed. 32. An express train is traveling at a speed of 420mph. How far can it travel in 3 hours? 33. Mitchell is running at a speed of 6m/sec. How long will it take to run 300m? 34. A train left Station X at 8:30AM for Station Y. The distance between the two stations was 250km. At what time would it reach Station Y if its average speed was 100km? 35. Ryan took 15 minutes to walk to school at an average speed of 70m/min. His brother took 20 minutes to walk the same distance. Find his brother s average speed. 36. Daniel took 2 hours to drive from Town A to Town B at an average speed of 60km/h. How long would he take if he drove at an average speed of 80km/h.
37. Cameron took 8 minutes to run around a 400 meter track 4 times. Find his average speed in meters/min. 38. A car left Town A at 9:30AM and reached Town B at 11:30AM Its average speed was 60km/h. Find the distance between Town A and Town B. 39. The distance between Marisa s house and the post office is 720m. If she walks from her house to the post office at an average speed of 80m/min, how long will she take? 40. The diagram shows the route of a bus from Town A to Town D. A 22.5km B 42.8km C 42.7km D x x x x The bus left Town A at 2:30PM and arrived at Town D at 4:30PM. What was his average Speed for the trip? 41. Danny took 2 hours to cycle from Town A to Town B. His average speed was 10km/h. A. Find the distance between the two towns. B. If his average was increased by 2km/h, how much time would he take for the trip? 42. Ben and David both cycled a distance of 24km. They started at the same time. David completed the trip 20 minutes earlier than Ben. If David s average speed was 9km/h., find Ben s average speed. 43. Paul took 5 minutes to walk from his house to the main road at an average speed of 46m/min. He then took another 10 minutes to walk to his office at 40m/min. How far did he walk altogether? 44. A group of boys went on a 12 km hike. For the first 3 km, they walked at an average speed of 4km/h. For the rest of the hike, they walked at an average speed of 6km/h. Find the total time taken. 45. Andrew drove from Town X to Town Y. He took 2 hours to travel 4/5 of the trip. He took 1 hour to travel the remaining 30km. A. Find the distance between the two towns. B. Find his average speed for the whole trip. 46. A motorist traveled from Town P to Town Q. After traveling 1/3 of the trip at an average speed of 45km/h, he continued to travel another 240km to reach Town Q. A.Find the distance between the two towns. B.If his average speed for the whole trip was 54km/h, find his average speed for the last 2/32/3 of the trip.
47. Tine took2 hours to drive from Town P to Town Q at an average speed of 70km/h. On her way back, she drove at an average speed of 80km/h. If she left Town Q at 3:00 PM, what time did she reach Town P? 48. A van and a car both traveled a distance of 190km from Rose Town to Orchid Town. The car left Rose Town 50 minutes before the van, but arrived at Orchid Town 20 minutes earlier than the van. If the average speed of the van was 60km/h, find the average speed of the car. 49. Ricardo drove a distance of 120km from Town P to Town Q at an average speed of 40km/h. On his way back, he drove at an average speed of 60km/h. Fins his average speed for the whole trip. 50. Mr. Jackson drove a distance of 250km from Town A to Town B. He left Town A at 9:00AM and arrived at Town B at 1:30PM. If his average speed for the first 3/5 of the trip was 60km/h, find his average speed for the remaining trip. 51. Nicky drove from Town X to Town Y. He took 1/2 hour to cover 1/4 of the trip at an average speed of 70km/h. How long did he take to cover the remaining trip if his average speed for the whole trip was 80km/h? 52. Mr. Banks drove a distance of 80km from Town X to Town Y. For the first 40 minutes, he drove at an average speed of 72km/h. His average speed for the remaining trip was 64km/h. If he arrived at Town Y at 10:00AM, what time did he leave Town X? 53. Two Towns, A and B, are 20km apart. At 12:00 noon, Peter left Town A and cycled towards Town B at 15km/h. At the same time, Henry left Town B and cycled towards Town A at 12km/h along the same road. Find the distance between Peter and Henry at 12:40PM. 54. As part of a training program for the Boston Marathon, a runner wants to build endurance by running at a rate of 9mph for 20 minutes. How far will the runner travel in that time? 55. It takes a hospital dietician 40 minutes to drive from home to the hospital, a distance of 20 miles. What is the dietician s average rate of speed? 56. The Ride For Health Bicycle Club has chosen a 36 mile course for this Saturday s ride. If the riders plan on averaging 12mph while they are riding, and they take a one hour lunch, how long will it take them to complete the trip? 57. Marcella leaves home at 9:00AM and drives to school, arriving at 9:45AM If the distance between home and school is 27 miles, what is Marcella s average rate of speed? 58. Palmer s average running speed is 3km/h faster than his average walking speed. If Palmer can run around a 30km course in 2 hours, how many hours would it take for Palmer to walk the same course?
59. Two cyclists start from the same point at the same time and move in opposite directions. One cyclist is traveling at 8mph, and the other cyclist is traveling at 9mph. After 30 minutes how far apart are the two cyclists? 60. At 8:00AM a train leaves a station and travels at a rate of 45mph. At 9:00Amm a second train leaves the same station on the same track and travels in the direction of the first train at a speed of 60mph. At 10:00AM, how far apart are the two trains?