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 4 km head start and moves at 12 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 10 km head start and moves at 4 km/h. Runner B chases in the same direction at 6 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 10 km head start and moves at 5 km/h. Runner B chases in the same direction at 10 km/h. How many hours will it take Runner B to catch Runner A?
4. Runner A has a 18 km head start and moves at 10 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?
5. Runner A has a 63 km head start and moves at 7 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
6. Runner A has a 70 km head start and moves at 4 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 28 km head start and moves at 4 km/h. Runner B chases in the same direction at 11 km/h. How many hours will it take Runner B to catch Runner A?
8. Runner A has a 55 km head start and moves at 16 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?
9. Runner A has a 50 km head start and moves at 6 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
10. Runner A has a 24 km head start and moves at 14 km/h. Runner B chases in the same direction at 26 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 20 km head start and moves at 14 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?
12. Runner A has a 72 km head start and moves at 5 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?

12 questions · Seed 55 · 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 4 km head start and moves at 12 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 14 − 12 = 2 km/h. Time = 4 km ÷ 2 km/h = 2 hours.
2. Runner A has a 10 km head start and moves at 4 km/h. Runner B chases in the same direction at 6 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 6 − 4 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.
3. Runner A has a 10 km head start and moves at 5 km/h. Runner B chases in the same direction at 10 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 10 − 5 = 5 km/h. Time = 10 km ÷ 5 km/h = 2 hours.
4. Runner A has a 18 km head start and moves at 10 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?
9 hours
Relative closing speed = 12 − 10 = 2 km/h. Time = 18 km ÷ 2 km/h = 9 hours.
5. Runner A has a 63 km head start and moves at 7 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 16 − 7 = 9 km/h. Time = 63 km ÷ 9 km/h = 7 hours.
6. Runner A has a 70 km head start and moves at 4 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 14 − 4 = 10 km/h. Time = 70 km ÷ 10 km/h = 7 hours.
7. Runner A has a 28 km head start and moves at 4 km/h. Runner B chases in the same direction at 11 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 11 − 4 = 7 km/h. Time = 28 km ÷ 7 km/h = 4 hours.
8. Runner A has a 55 km head start and moves at 16 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 − 16 = 11 km/h. Time = 55 km ÷ 11 km/h = 5 hours.
9. Runner A has a 50 km head start and moves at 6 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 16 − 6 = 10 km/h. Time = 50 km ÷ 10 km/h = 5 hours.
10. Runner A has a 24 km head start and moves at 14 km/h. Runner B chases in the same direction at 26 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 26 − 14 = 12 km/h. Time = 24 km ÷ 12 km/h = 2 hours.
11. Runner A has a 20 km head start and moves at 14 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?
5 hours
Relative closing speed = 18 − 14 = 4 km/h. Time = 20 km ÷ 4 km/h = 5 hours.
12. Runner A has a 72 km head start and moves at 5 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?
6 hours
Relative closing speed = 17 − 5 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

12 questions · Seed 55 · 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 4 km head start and moves at 12 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 10 km head start and moves at 4 km/h. Runner B chases in the same direction at 6 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 10 km head start and moves at 5 km/h. Runner B chases in the same direction at 10 km/h. How many hours will it take Runner B to catch Runner A?
4. Runner A has a 18 km head start and moves at 10 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?
5. Runner A has a 63 km head start and moves at 7 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
6. Runner A has a 70 km head start and moves at 4 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 28 km head start and moves at 4 km/h. Runner B chases in the same direction at 11 km/h. How many hours will it take Runner B to catch Runner A?
8. Runner A has a 55 km head start and moves at 16 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?
9. Runner A has a 50 km head start and moves at 6 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
10. Runner A has a 24 km head start and moves at 14 km/h. Runner B chases in the same direction at 26 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 20 km head start and moves at 14 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?
12. Runner A has a 72 km head start and moves at 5 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?

12 questions · Seed 55 · 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 4 km head start and moves at 12 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 14 − 12 = 2 km/h. Time = 4 km ÷ 2 km/h = 2 hours.
2. Runner A has a 10 km head start and moves at 4 km/h. Runner B chases in the same direction at 6 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 6 − 4 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.
3. Runner A has a 10 km head start and moves at 5 km/h. Runner B chases in the same direction at 10 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 10 − 5 = 5 km/h. Time = 10 km ÷ 5 km/h = 2 hours.
4. Runner A has a 18 km head start and moves at 10 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?
9 hours
Relative closing speed = 12 − 10 = 2 km/h. Time = 18 km ÷ 2 km/h = 9 hours.
5. Runner A has a 63 km head start and moves at 7 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 16 − 7 = 9 km/h. Time = 63 km ÷ 9 km/h = 7 hours.
6. Runner A has a 70 km head start and moves at 4 km/h. Runner B chases in the same direction at 14 km/h. How many hours will it take Runner B to catch Runner A?
7 hours
Relative closing speed = 14 − 4 = 10 km/h. Time = 70 km ÷ 10 km/h = 7 hours.
7. Runner A has a 28 km head start and moves at 4 km/h. Runner B chases in the same direction at 11 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 11 − 4 = 7 km/h. Time = 28 km ÷ 7 km/h = 4 hours.
8. Runner A has a 55 km head start and moves at 16 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 − 16 = 11 km/h. Time = 55 km ÷ 11 km/h = 5 hours.
9. Runner A has a 50 km head start and moves at 6 km/h. Runner B chases in the same direction at 16 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 16 − 6 = 10 km/h. Time = 50 km ÷ 10 km/h = 5 hours.
10. Runner A has a 24 km head start and moves at 14 km/h. Runner B chases in the same direction at 26 km/h. How many hours will it take Runner B to catch Runner A?
2 hours
Relative closing speed = 26 − 14 = 12 km/h. Time = 24 km ÷ 12 km/h = 2 hours.
11. Runner A has a 20 km head start and moves at 14 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?
5 hours
Relative closing speed = 18 − 14 = 4 km/h. Time = 20 km ÷ 4 km/h = 5 hours.
12. Runner A has a 72 km head start and moves at 5 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?
6 hours
Relative closing speed = 17 − 5 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

12 questions · Seed 55 · Age guidance, not curriculum certification