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 56 km head start and moves at 6 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 36 km head start and moves at 14 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 81 km head start and moves at 9 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?
4. Runner A has a 60 km head start and moves at 7 km/h. Runner B chases in the same direction at 19 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 4 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?
6. Runner A has a 36 km head start and moves at 18 km/h. Runner B chases in the same direction at 24 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 24 km head start and moves at 15 km/h. Runner B chases in the same direction at 23 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 18 km/h. Runner B chases in the same direction at 30 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 10 km head start and moves at 16 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 45 km head start and moves at 6 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?
11. Runner A has a 81 km head start and moves at 13 km/h. Runner B chases in the same direction at 22 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 45 km head start and moves at 13 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 47 · 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 56 km head start and moves at 6 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 − 6 = 8 km/h. Time = 56 km ÷ 8 km/h = 7 hours.
2. Runner A has a 36 km head start and moves at 14 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 23 − 14 = 9 km/h. Time = 36 km ÷ 9 km/h = 4 hours.
3. Runner A has a 81 km head start and moves at 9 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?
9 hours
Relative closing speed = 18 − 9 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.
4. Runner A has a 60 km head start and moves at 7 km/h. Runner B chases in the same direction at 19 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 19 − 7 = 12 km/h. Time = 60 km ÷ 12 km/h = 5 hours.
5. Runner A has a 18 km head start and moves at 4 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?
3 hours
Relative closing speed = 10 − 4 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.
6. Runner A has a 36 km head start and moves at 18 km/h. Runner B chases in the same direction at 24 km/h. How many hours will it take Runner B to catch Runner A?
6 hours
Relative closing speed = 24 − 18 = 6 km/h. Time = 36 km ÷ 6 km/h = 6 hours.
7. Runner A has a 24 km head start and moves at 15 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 23 − 15 = 8 km/h. Time = 24 km ÷ 8 km/h = 3 hours.
8. Runner A has a 48 km head start and moves at 18 km/h. Runner B chases in the same direction at 30 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 30 − 18 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.
9. Runner A has a 10 km head start and moves at 16 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 − 16 = 5 km/h. Time = 10 km ÷ 5 km/h = 2 hours.
10. Runner A has a 45 km head start and moves at 6 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 − 6 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
11. Runner A has a 81 km head start and moves at 13 km/h. Runner B chases in the same direction at 22 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 22 − 13 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.
12. Runner A has a 45 km head start and moves at 13 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?
9 hours
Relative closing speed = 18 − 13 = 5 km/h. Time = 45 km ÷ 5 km/h = 9 hours.

12 questions · Seed 47 · 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 56 km head start and moves at 6 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 36 km head start and moves at 14 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
3. Runner A has a 81 km head start and moves at 9 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?
4. Runner A has a 60 km head start and moves at 7 km/h. Runner B chases in the same direction at 19 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 4 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?
6. Runner A has a 36 km head start and moves at 18 km/h. Runner B chases in the same direction at 24 km/h. How many hours will it take Runner B to catch Runner A?
7. Runner A has a 24 km head start and moves at 15 km/h. Runner B chases in the same direction at 23 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 18 km/h. Runner B chases in the same direction at 30 km/h. How many hours will it take Runner B to catch Runner A?
9. Runner A has a 10 km head start and moves at 16 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 45 km head start and moves at 6 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?
11. Runner A has a 81 km head start and moves at 13 km/h. Runner B chases in the same direction at 22 km/h. How many hours will it take Runner B to catch Runner A?
12. Runner A has a 45 km head start and moves at 13 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 47 · 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 56 km head start and moves at 6 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 − 6 = 8 km/h. Time = 56 km ÷ 8 km/h = 7 hours.
2. Runner A has a 36 km head start and moves at 14 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 23 − 14 = 9 km/h. Time = 36 km ÷ 9 km/h = 4 hours.
3. Runner A has a 81 km head start and moves at 9 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?
9 hours
Relative closing speed = 18 − 9 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.
4. Runner A has a 60 km head start and moves at 7 km/h. Runner B chases in the same direction at 19 km/h. How many hours will it take Runner B to catch Runner A?
5 hours
Relative closing speed = 19 − 7 = 12 km/h. Time = 60 km ÷ 12 km/h = 5 hours.
5. Runner A has a 18 km head start and moves at 4 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?
3 hours
Relative closing speed = 10 − 4 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.
6. Runner A has a 36 km head start and moves at 18 km/h. Runner B chases in the same direction at 24 km/h. How many hours will it take Runner B to catch Runner A?
6 hours
Relative closing speed = 24 − 18 = 6 km/h. Time = 36 km ÷ 6 km/h = 6 hours.
7. Runner A has a 24 km head start and moves at 15 km/h. Runner B chases in the same direction at 23 km/h. How many hours will it take Runner B to catch Runner A?
3 hours
Relative closing speed = 23 − 15 = 8 km/h. Time = 24 km ÷ 8 km/h = 3 hours.
8. Runner A has a 48 km head start and moves at 18 km/h. Runner B chases in the same direction at 30 km/h. How many hours will it take Runner B to catch Runner A?
4 hours
Relative closing speed = 30 − 18 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.
9. Runner A has a 10 km head start and moves at 16 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 − 16 = 5 km/h. Time = 10 km ÷ 5 km/h = 2 hours.
10. Runner A has a 45 km head start and moves at 6 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 − 6 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.
11. Runner A has a 81 km head start and moves at 13 km/h. Runner B chases in the same direction at 22 km/h. How many hours will it take Runner B to catch Runner A?
9 hours
Relative closing speed = 22 − 13 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.
12. Runner A has a 45 km head start and moves at 13 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?
9 hours
Relative closing speed = 18 − 13 = 5 km/h. Time = 45 km ÷ 5 km/h = 9 hours.

12 questions · Seed 47 · Age guidance, not curriculum certification