Time, Rate, and Distance Word Problems

Respect   Responsibility   Readiness

1. A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a passenger train leaves the same station for Chicago traveling at 60 mph. How long will it be before the passenger train overtakes the freight train?

2. A car leaves San Francisco for Los Angeles traveling an average of 70 mph. At the same time, another car leaves Los Angeles for San Francisco traveling 60 mph. If it is 520 miles between San Francisco and Los Angeles, how long before the two cars meet, assuming that each maintains its average speed?

3. Two planes leave New York at 10 A.M., one heading for Europe at 600 mph and one heading in the opposite direction at 150 mph. At what time will they be 900 miles apart? How far has each traveled?

4. Moe Tell makes a business trip from his house to Logan in 2 hours. One hour later, he returns home in traffic at a rate 20 mph less than his rate going. If Moe is gone a total of 6 hours, how fast did he travel on each leg of the trip?

5. Tom and Jerry went on a camping trip with their motorcycles. One day Jerry left camp on his motorcycle to go to the village. Ten minutes later Tom decided to go too. If Jerry was traveling 30 mph and Tom traveled 35 mph, how long was it before Tom caught up with Jerry?

6. Two cars headed for Las Vegas. One is 50 miles ahead of the other on the same road. The one in front is traveling 60 mph while the second car is traveling 70 mph. How long will it be before the second car overtakes the first car?

7. The Red Baron takes 5 hours to fly from Los Angeles to Honolulu and 4 1/11 hours to return from Honolulu to Los Angeles. If the wind velocity is 50 mph from the west on both trips, what is the airspeed of the plane? (Airspeed is the speed of the plane in still air)

8. In his motorboat, Don Stream can go downstream in 1 hour less time than he can go upstream the same distance. If the current is 5 mph, how fast can Don travel in still water if it takes him 2 hours to travel upstream the given distance?

9. Kay Oss leaves Seattle for New York in her car, averaging 80 mph across open country. One hour later a plane leaves Seattle for New York following the same route and flying 400 mph. How long will it be before the plane overtakes the car?

10. A train averaging 50 mph leaves San Francisco at I P.M. for Los Angeles 440 miles away. At the same time a second train leaves Los Angeles headed for San Francisco on the same track and traveling at an average rate of 60 mph. At what times does the accident occur?

11. Doug Upp rides his bike at 6 mph to the bus station. He then rides the bus to work, averaging 30 mph. If he spends 20 minutes less time on the bus than on the bike, and the distance from his house to work is 26 miles, what is the distance from his house to the bus station?

12. Two planes leave Kansas City at I P.M. Plane A heads east at 450 mph and plane B heads due west at 600 mph. How long will it be before the planes are 2100 miles apart?

13. Doomtown is 200 miles due west of Sagebrush, and Joshua is due west of Doomtown. At 9 A.M. Mr. White leaves Sagebrush for Joshua. At I P.M. Mr. Earp leaves Doomtown for Joshua. If Mr. Earp travels at an average speed 20 mph faster than Mr. White and they each reach Joshua at 4 P.M., how fast is each traveling?

14. Meg A. Bucks left Rome at 8 A.M. and drove her Ferrari at 80 mph from Rome to Sorrento. She then took the boat to Capri for the day, returning to Sorrento 5 hours later. On the return trip from Sorrento to Rome she averaged 60 mph and arrived in Rome at 8 P.M. How far is it from Rome to Sorrento?

15. Superman flies to San Francisco from Santa Barbara in 3 hours. He flies back in 2 hours. If the wind was blowing from the north at a velocity of 40 mph going, but changed to 20 mph from the north returning, what was the airspeed of superman (his speed in still air)?

16. Phil T. Rich leaves home for Fresno 400 miles away. After 2 hours, he has to reduce his speed by 20 mph due to rain. If he takes I hour for lunch and gas and reaches Fresno 9 hours after he left home, what was his initial speed?

17. A highway patrolman spots a speeding car. He clocks it at 70 mph and takes off after it 0.5 mile behind. If the patrolman travels at an average rate of 90 mph, how long will it be before he overtakes the car?

18. Boy Scouts hiking in the mountains divide into two groups to hike around Lake Sahara. They leave the same place at 10 A.M., and one group of younger boys hikes east around the lake and the older group hikes west. If the younger boys hike at a rate of 3 mph and the older boys hike at a rate of 5 mph, how long before they meet on the other side of the lake if the trail around the lake is 8 miles long? At what time do they meet?

19. A boat has a speed of I 5 mph in still water. It travels downstream from Greentown to Bluetown in two-fifths of an hour. It then goes back upstream from Bluetown to Redtown, which is 2 miles down­stream from Greentown, in three-fifths of an hour. Find the rate of the current.

20. Calvin can run a mile in 6 minutes. Hobbes can run a mile in 8 minutes. If Hobbes goes out to practice and starts I minute before Calvin starts on his practice run, will Calvin catch up with Hobbes before he reaches the mile marker? (Assume a straight track and average speed.)

22. Harry and Kerry started from the same point at the same time. They traveled in opposite directions on their bicycles. Harry traveled at the rate of 9 km/h, and Kerry traveled at 11 km/h. After how many hours were they 60 km apart?

23. Two trains leave Trackville at the same time. One travels north at 90 km/h. The other travels south at 110 km/h. After how many hours will the trains be 900 km apart?

24. Two steamships sailing in opposite directions pass each other. One ship is sailing at 32 knots (nautical miles per hour). The other ship is sailing at 28 knots After how many hours will the ships be 1 50 nautical miles apart?

25. Two jets are traveling toward each other and are 3400 km apart. One jet is flying at 875 km/h. The other jet is flying at 825 km/h. In how many hours will the jets pass each other?

26. A train left Podunk and traveled west at 70 km/h. Two hours later, another train left Podunk and traveled east at 90 km/h. How many hours had the first train traveled when they were 1420 km apart?

27. A train left Podunk and traveled north at 75 km/h. Two hours later, another train left Podunk and traveled in the same direction at 100 km/h. How many hours had the first train traveled when the second train overtook it?

28. Joe Spout left a campsite on a trip down the river in a canoe, traveling at 6 km/h. Four hours later, Joe’s lather set out after him in a motorboat. The motorboat traveled at 30 km/h. How long after Joe’s father started did he overtake the canoe?

In the question above, how far had Joe traveled down the river when his father overtook him?

29. Two trucks left Bucks Trucks traveling in opposite directions. One truck traveled at a rate of 70 km/h. the other at 80 km/h. After how many hours were the trucks 900 km apart?

30. A truck left Hucks Trucks and traveled north at 80 km ft One hour later, another truck left Hucks Trucks and traveled south at 60 km/h. How many hours had the first truck traveled when they were 150 km apart?

31. Steve McSpoke left home on his bicycle at 8:00 A.M., traveling at 18 km h. At 10:00 A.M., Steves brother set out after him on a motorcycle, following the same route. The motorcycle traveled at 54 km/h. How long had Steve traveled when his brother overtook him?

In Exercise 31, how far had Steve traveled when his brother overtook him?

32. Dr. Pepper left Oakville at 9:00 A.M. and drove to Central City at 60 km/h. H. Salt left Oakville at 11:00 A.M. and traveled the same route to Central City. If both men arrived in Central City at 4:00 P.M., at what rate did H. Salt travel?

33. Two jets are traveling toward each other and are 4000 km apart. The rate of one jet is 1 00 km h faster than the rate of the other. If the jets pass each other after 2.5 hours, what is the rate of the faster jet?

34. Ms. Driva Reck drove from her home to a service station at 48 km h. She returned home by bicycle at 16 km h. The entire trip took 4 hours. How far was the service station from Ms. Recks home?

35. A plane on a search mission flew east from an airport, turned, and flew west back to the airport. The plane cruised at 300 km/h when flying east, and 400 km/h when flying west. The plane was in the air for 7 hours. How far from the airport did the plane travel?

36. A motorboat can travel upstream on a river at 18 km/h and downstream at 30 km h. How far upstream can the boat travel if it leaves at 8:00 A.M. and must return by noon?

37. A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water? What is the rate of the current?

38. When a plane flies into the wind, it can travel 3000 km in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.

39. When Lucy swims with the current, she swims 18km in 2 hours. Against the current, she can swim only 14 km in the same time. How fast can Lucy swim in still water? What is the rate of the current?

40. With the wind, a jet can fly 2500 km in 2 h 30 mm. Against the wind, it can fly only 2000 km in the same time. Find the rate of the jet in still air and the rate of the wind.

41. On an upstream trip, a canoe travels 40 km in 5 hours. Downstream, it travels the same distance in half the time. What is the rate of the canoe in still water and the rate of the current?

42. A duck can fly 2400 m in 10 mm with the wind. Against the wind, t can fly only two thirds of this distance in 10 mm. How fast could the duck fly in still air? What is the rate of the wind?

43. With the wind, a plane flew 1400 km in 4 hours. On the return trip, the pilot was forced to land after 1 h 30 mm, having traveled only 450 km. Find the rate of the plane in still air and the rate of the wind.

44. A salmon swims 100 m in 8 min downstream. Upstream, it would take the fish 20 min to swim the same distance. What is the rate of the salmon in still water? What is the rate of the current?