ReasoningAges 13-15

Relative speed & pursuit puzzles

Use relative closing speed to calculate how long it takes a faster runner or vehicle to close a head start. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Relative speed & pursuit puzzles

Take your time. Show your thinking.

1. Runner A has a 18 km head start and moves at 15 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 24 km head start and moves at 13 km/h. Runner B chases in the same direction at 25 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 45 km head start and moves at 18 km/h. Runner B chases in the same direction at 27 km/h. How many hours will it take Runner B to catch Runner A?
4. Runner A has a 33 km head start and moves at 6 km/h. Runner B chases in the same direction at 17 km/h. How many hours will it take Runner B to catch Runner A?
5. Runner A has a 14 km head start and moves at 14 km/h. Runner B chases in the same direction at 21 km/h. How many hours will it take Runner B to catch Runner A?
6. Runner A has a 90 km head start and moves at 10 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 10 km head start and moves at 18 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
8. Runner A has a 32 km head start and moves at 12 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 21 km head start and moves at 9 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
10. Runner A has a 36 km head start and moves at 6 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 108 km head start and moves at 17 km/h. Runner B chases in the same direction at 29 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 28 km head start and moves at 8 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?

12 questions · Seed 52 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

1. Runner A has a 18 km head start and moves at 15 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
6 hours
Relative closing speed = 18 − 15 = 3 km/h. Time = 18 km ÷ 3 km/h = 6 hours.
2. Runner A has a 24 km head start and moves at 13 km/h. Runner B chases in the same direction at 25 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 25 − 13 = 12 km/h. Time = 24 km ÷ 12 km/h = 2 hours.
3. Runner A has a 45 km head start and moves at 18 km/h. Runner B chases in the same direction at 27 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 27 − 18 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
4. Runner A has a 33 km head start and moves at 6 km/h. Runner B chases in the same direction at 17 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 17 − 6 = 11 km/h. Time = 33 km ÷ 11 km/h = 3 hours.
5. Runner A has a 14 km head start and moves at 14 km/h. Runner B chases in the same direction at 21 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 21 − 14 = 7 km/h. Time = 14 km ÷ 7 km/h = 2 hours.
6. Runner A has a 90 km head start and moves at 10 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 20 − 10 = 10 km/h. Time = 90 km ÷ 10 km/h = 9 hours.
7. Runner A has a 10 km head start and moves at 18 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 20 − 18 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.
8. Runner A has a 32 km head start and moves at 12 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 20 − 12 = 8 km/h. Time = 32 km ÷ 8 km/h = 4 hours.
9. Runner A has a 21 km head start and moves at 9 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 12 − 9 = 3 km/h. Time = 21 km ÷ 3 km/h = 7 hours.
10. Runner A has a 36 km head start and moves at 6 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 18 − 6 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
11. Runner A has a 108 km head start and moves at 17 km/h. Runner B chases in the same direction at 29 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 29 − 17 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.
12. Runner A has a 28 km head start and moves at 8 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 12 − 8 = 4 km/h. Time = 28 km ÷ 4 km/h = 7 hours.

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Relative speed & pursuit puzzles

Take your time. Show your thinking.

1. Runner A has a 18 km head start and moves at 15 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 24 km head start and moves at 13 km/h. Runner B chases in the same direction at 25 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 45 km head start and moves at 18 km/h. Runner B chases in the same direction at 27 km/h. How many hours will it take Runner B to catch Runner A?
4. Runner A has a 33 km head start and moves at 6 km/h. Runner B chases in the same direction at 17 km/h. How many hours will it take Runner B to catch Runner A?
5. Runner A has a 14 km head start and moves at 14 km/h. Runner B chases in the same direction at 21 km/h. How many hours will it take Runner B to catch Runner A?
6. Runner A has a 90 km head start and moves at 10 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 10 km head start and moves at 18 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
8. Runner A has a 32 km head start and moves at 12 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 21 km head start and moves at 9 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
10. Runner A has a 36 km head start and moves at 6 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 108 km head start and moves at 17 km/h. Runner B chases in the same direction at 29 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 28 km head start and moves at 8 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

1. Runner A has a 18 km head start and moves at 15 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
6 hours
Relative closing speed = 18 − 15 = 3 km/h. Time = 18 km ÷ 3 km/h = 6 hours.
2. Runner A has a 24 km head start and moves at 13 km/h. Runner B chases in the same direction at 25 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 25 − 13 = 12 km/h. Time = 24 km ÷ 12 km/h = 2 hours.
3. Runner A has a 45 km head start and moves at 18 km/h. Runner B chases in the same direction at 27 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 27 − 18 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
4. Runner A has a 33 km head start and moves at 6 km/h. Runner B chases in the same direction at 17 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 17 − 6 = 11 km/h. Time = 33 km ÷ 11 km/h = 3 hours.
5. Runner A has a 14 km head start and moves at 14 km/h. Runner B chases in the same direction at 21 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 21 − 14 = 7 km/h. Time = 14 km ÷ 7 km/h = 2 hours.
6. Runner A has a 90 km head start and moves at 10 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 20 − 10 = 10 km/h. Time = 90 km ÷ 10 km/h = 9 hours.
7. Runner A has a 10 km head start and moves at 18 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 20 − 18 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.
8. Runner A has a 32 km head start and moves at 12 km/h. Runner B chases in the same direction at 20 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 20 − 12 = 8 km/h. Time = 32 km ÷ 8 km/h = 4 hours.
9. Runner A has a 21 km head start and moves at 9 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 12 − 9 = 3 km/h. Time = 21 km ÷ 3 km/h = 7 hours.
10. Runner A has a 36 km head start and moves at 6 km/h. Runner B chases in the same direction at 18 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 18 − 6 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
11. Runner A has a 108 km head start and moves at 17 km/h. Runner B chases in the same direction at 29 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 29 − 17 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.
12. Runner A has a 28 km head start and moves at 8 km/h. Runner B chases in the same direction at 12 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 12 − 8 = 4 km/h. Time = 28 km ÷ 4 km/h = 7 hours.

12 questions · Seed 52 · Age guidance, not curriculum certification