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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Age band:Ages 10-12 Ages 13-15

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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 12 km head start and moves at 13 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?
2. Runner A has a 40 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?
3. Runner A has a 45 km head start and moves at 16 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?
4. Runner A has a 12 km head start and moves at 10 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?
5. Runner A has a 18 km head start and moves at 6 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?
6. Runner A has a 30 km head start and moves at 12 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?
7. Runner A has a 64 km head start and moves at 10 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?
8. Runner A has a 30 km head start and moves at 9 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 32 km head start and moves at 17 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?
10. Runner A has a 36 km head start and moves at 16 km/h. Runner B chases in the same direction at 28 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 80 km head start and moves at 5 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 35 km head start and moves at 13 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?

12 questions · Seed 104734 · 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 12 km head start and moves at 13 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 − 13 = 4 km/h. Time = 12 km ÷ 4 km/h = 3 hours.
2. Runner A has a 40 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?
5 hours
Relative closing speed = 20 − 12 = 8 km/h. Time = 40 km ÷ 8 km/h = 5 hours.
3. Runner A has a 45 km head start and moves at 16 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?
5 hours
Relative closing speed = 25 − 16 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
4. Runner A has a 12 km head start and moves at 10 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?
3 hours
Relative closing speed = 14 − 10 = 4 km/h. Time = 12 km ÷ 4 km/h = 3 hours.
5. Runner A has a 18 km head start and moves at 6 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?
3 hours
Relative closing speed = 12 − 6 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.
6. Runner A has a 30 km head start and moves at 12 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 − 12 = 6 km/h. Time = 30 km ÷ 6 km/h = 5 hours.
7. Runner A has a 64 km head start and moves at 10 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?
8 hours
Relative closing speed = 18 − 10 = 8 km/h. Time = 64 km ÷ 8 km/h = 8 hours.
8. Runner A has a 30 km head start and moves at 9 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 15 − 9 = 6 km/h. Time = 30 km ÷ 6 km/h = 5 hours.
9. Runner A has a 32 km head start and moves at 17 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?
8 hours
Relative closing speed = 21 − 17 = 4 km/h. Time = 32 km ÷ 4 km/h = 8 hours.
10. Runner A has a 36 km head start and moves at 16 km/h. Runner B chases in the same direction at 28 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 28 − 16 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
11. Runner A has a 80 km head start and moves at 5 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 15 − 5 = 10 km/h. Time = 80 km ÷ 10 km/h = 8 hours.
12. Runner A has a 35 km head start and moves at 13 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 − 13 = 7 km/h. Time = 35 km ÷ 7 km/h = 5 hours.

12 questions · Seed 104734 · 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 12 km head start and moves at 13 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?
2. Runner A has a 40 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?
3. Runner A has a 45 km head start and moves at 16 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?
4. Runner A has a 12 km head start and moves at 10 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?
5. Runner A has a 18 km head start and moves at 6 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?
6. Runner A has a 30 km head start and moves at 12 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?
7. Runner A has a 64 km head start and moves at 10 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?
8. Runner A has a 30 km head start and moves at 9 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 32 km head start and moves at 17 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?
10. Runner A has a 36 km head start and moves at 16 km/h. Runner B chases in the same direction at 28 km/h. How many hours will it take Runner B to catch Runner A?
11. Runner A has a 80 km head start and moves at 5 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 35 km head start and moves at 13 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?

12 questions · Seed 104734 · 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 12 km head start and moves at 13 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 − 13 = 4 km/h. Time = 12 km ÷ 4 km/h = 3 hours.
2. Runner A has a 40 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?
5 hours
Relative closing speed = 20 − 12 = 8 km/h. Time = 40 km ÷ 8 km/h = 5 hours.
3. Runner A has a 45 km head start and moves at 16 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?
5 hours
Relative closing speed = 25 − 16 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
4. Runner A has a 12 km head start and moves at 10 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?
3 hours
Relative closing speed = 14 − 10 = 4 km/h. Time = 12 km ÷ 4 km/h = 3 hours.
5. Runner A has a 18 km head start and moves at 6 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?
3 hours
Relative closing speed = 12 − 6 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.
6. Runner A has a 30 km head start and moves at 12 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 − 12 = 6 km/h. Time = 30 km ÷ 6 km/h = 5 hours.
7. Runner A has a 64 km head start and moves at 10 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?
8 hours
Relative closing speed = 18 − 10 = 8 km/h. Time = 64 km ÷ 8 km/h = 8 hours.
8. Runner A has a 30 km head start and moves at 9 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 15 − 9 = 6 km/h. Time = 30 km ÷ 6 km/h = 5 hours.
9. Runner A has a 32 km head start and moves at 17 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?
8 hours
Relative closing speed = 21 − 17 = 4 km/h. Time = 32 km ÷ 4 km/h = 8 hours.
10. Runner A has a 36 km head start and moves at 16 km/h. Runner B chases in the same direction at 28 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 28 − 16 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
11. Runner A has a 80 km head start and moves at 5 km/h. Runner B chases in the same direction at 15 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 15 − 5 = 10 km/h. Time = 80 km ÷ 10 km/h = 8 hours.
12. Runner A has a 35 km head start and moves at 13 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 − 13 = 7 km/h. Time = 35 km ÷ 7 km/h = 5 hours.

12 questions · Seed 104734 · Age guidance, not curriculum certification