ReasoningAges 10-12

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 10-12

Relative speed & pursuit puzzles

Take your time. Show your thinking.

1. Runner A has a 30 km head start and moves at 10 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?
2. Runner A has a 14 km head start and moves at 11 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. Runner A has a 36 km head start and moves at 8 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. Runner A has a 16 km head start and moves at 7 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. Runner A has a 8 km head start and moves at 11 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?
6. Runner A has a 48 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?
7. Runner A has a 18 km head start and moves at 12 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. Runner A has a 48 km head start and moves at 7 km/h. Runner B chases in the same direction at 13 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 45 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?
10. Runner A has a 9 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?
11. Runner A has a 72 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?
12. Runner A has a 16 km head start and moves at 16 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 questions · Seed 43 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

1. Runner A has a 30 km head start and moves at 10 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?
6 hours
Relative closing speed = 15 − 10 = 5 km/h. Time = 30 km ÷ 5 km/h = 6 hours.
2. Runner A has a 14 km head start and moves at 11 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 hours
Relative closing speed = 18 − 11 = 7 km/h. Time = 14 km ÷ 7 km/h = 2 hours.
3. Runner A has a 36 km head start and moves at 8 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 hours
Relative closing speed = 20 − 8 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
4. Runner A has a 16 km head start and moves at 7 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?
2 hours
Relative closing speed = 15 − 7 = 8 km/h. Time = 16 km ÷ 8 km/h = 2 hours.
5. Runner A has a 8 km head start and moves at 11 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?
2 hours
Relative closing speed = 15 − 11 = 4 km/h. Time = 8 km ÷ 4 km/h = 2 hours.
6. Runner A has a 48 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?
4 hours
Relative closing speed = 29 − 17 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.
7. Runner A has a 18 km head start and moves at 12 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 − 12 = 9 km/h. Time = 18 km ÷ 9 km/h = 2 hours.
8. Runner A has a 48 km head start and moves at 7 km/h. Runner B chases in the same direction at 13 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 13 − 7 = 6 km/h. Time = 48 km ÷ 6 km/h = 8 hours.
9. Runner A has a 45 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?
5 hours
Relative closing speed = 16 − 7 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
10. Runner A has a 9 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?
3 hours
Relative closing speed = 12 − 9 = 3 km/h. Time = 9 km ÷ 3 km/h = 3 hours.
11. Runner A has a 72 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?
8 hours
Relative closing speed = 25 − 16 = 9 km/h. Time = 72 km ÷ 9 km/h = 8 hours.
12. Runner A has a 16 km head start and moves at 16 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 − 16 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Relative speed & pursuit puzzles

Take your time. Show your thinking.

1. Runner A has a 30 km head start and moves at 10 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?
2. Runner A has a 14 km head start and moves at 11 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. Runner A has a 36 km head start and moves at 8 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. Runner A has a 16 km head start and moves at 7 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. Runner A has a 8 km head start and moves at 11 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?
6. Runner A has a 48 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?
7. Runner A has a 18 km head start and moves at 12 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. Runner A has a 48 km head start and moves at 7 km/h. Runner B chases in the same direction at 13 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 45 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?
10. Runner A has a 9 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?
11. Runner A has a 72 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?
12. Runner A has a 16 km head start and moves at 16 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 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

1. Runner A has a 30 km head start and moves at 10 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?
6 hours
Relative closing speed = 15 − 10 = 5 km/h. Time = 30 km ÷ 5 km/h = 6 hours.
2. Runner A has a 14 km head start and moves at 11 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 hours
Relative closing speed = 18 − 11 = 7 km/h. Time = 14 km ÷ 7 km/h = 2 hours.
3. Runner A has a 36 km head start and moves at 8 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 hours
Relative closing speed = 20 − 8 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
4. Runner A has a 16 km head start and moves at 7 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?
2 hours
Relative closing speed = 15 − 7 = 8 km/h. Time = 16 km ÷ 8 km/h = 2 hours.
5. Runner A has a 8 km head start and moves at 11 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?
2 hours
Relative closing speed = 15 − 11 = 4 km/h. Time = 8 km ÷ 4 km/h = 2 hours.
6. Runner A has a 48 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?
4 hours
Relative closing speed = 29 − 17 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.
7. Runner A has a 18 km head start and moves at 12 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 − 12 = 9 km/h. Time = 18 km ÷ 9 km/h = 2 hours.
8. Runner A has a 48 km head start and moves at 7 km/h. Runner B chases in the same direction at 13 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 13 − 7 = 6 km/h. Time = 48 km ÷ 6 km/h = 8 hours.
9. Runner A has a 45 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?
5 hours
Relative closing speed = 16 − 7 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
10. Runner A has a 9 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?
3 hours
Relative closing speed = 12 − 9 = 3 km/h. Time = 9 km ÷ 3 km/h = 3 hours.
11. Runner A has a 72 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?
8 hours
Relative closing speed = 25 − 16 = 9 km/h. Time = 72 km ÷ 9 km/h = 8 hours.
12. Runner A has a 16 km head start and moves at 16 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 − 16 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.

12 questions · Seed 43 · Age guidance, not curriculum certification