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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Age band:Ages 10-12 Ages 13-15

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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 16 km head start and moves at 13 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 96 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. Runner A has a 36 km head start and moves at 10 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?
4. Runner A has a 18 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. Runner A has a 6 km head start and moves at 16 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?
6. Runner A has a 33 km head start and moves at 12 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?
7. Runner A has a 50 km head start and moves at 18 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?
8. Runner A has a 18 km head start and moves at 8 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?
9. Runner A has a 28 km head start and moves at 9 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?
10. Runner A has a 40 km head start and moves at 14 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?
11. Runner A has a 24 km head start and moves at 7 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?
12. 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?

12 questions · Seed 58 · 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 16 km head start and moves at 13 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 − 13 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.
2. Runner A has a 96 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?
8 hours
Relative closing speed = 20 − 8 = 12 km/h. Time = 96 km ÷ 12 km/h = 8 hours.
3. Runner A has a 36 km head start and moves at 10 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?
3 hours
Relative closing speed = 22 − 10 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
4. Runner A has a 18 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?
9 hours
Relative closing speed = 6 − 4 = 2 km/h. Time = 18 km ÷ 2 km/h = 9 hours.
5. Runner A has a 6 km head start and moves at 16 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?
2 hours
Relative closing speed = 19 − 16 = 3 km/h. Time = 6 km ÷ 3 km/h = 2 hours.
6. Runner A has a 33 km head start and moves at 12 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 − 12 = 11 km/h. Time = 33 km ÷ 11 km/h = 3 hours.
7. Runner A has a 50 km head start and moves at 18 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?
5 hours
Relative closing speed = 28 − 18 = 10 km/h. Time = 50 km ÷ 10 km/h = 5 hours.
8. Runner A has a 18 km head start and moves at 8 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?
6 hours
Relative closing speed = 11 − 8 = 3 km/h. Time = 18 km ÷ 3 km/h = 6 hours.
9. Runner A has a 28 km head start and moves at 9 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?
7 hours
Relative closing speed = 13 − 9 = 4 km/h. Time = 28 km ÷ 4 km/h = 7 hours.
10. Runner A has a 40 km head start and moves at 14 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?
8 hours
Relative closing speed = 19 − 14 = 5 km/h. Time = 40 km ÷ 5 km/h = 8 hours.
11. Runner A has a 24 km head start and moves at 7 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?
8 hours
Relative closing speed = 10 − 7 = 3 km/h. Time = 24 km ÷ 3 km/h = 8 hours.
12. 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.

12 questions · Seed 58 · 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 16 km head start and moves at 13 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 96 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. Runner A has a 36 km head start and moves at 10 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?
4. Runner A has a 18 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. Runner A has a 6 km head start and moves at 16 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?
6. Runner A has a 33 km head start and moves at 12 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?
7. Runner A has a 50 km head start and moves at 18 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?
8. Runner A has a 18 km head start and moves at 8 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?
9. Runner A has a 28 km head start and moves at 9 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?
10. Runner A has a 40 km head start and moves at 14 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?
11. Runner A has a 24 km head start and moves at 7 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?
12. 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?

12 questions · Seed 58 · 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 16 km head start and moves at 13 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 − 13 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.
2. Runner A has a 96 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?
8 hours
Relative closing speed = 20 − 8 = 12 km/h. Time = 96 km ÷ 12 km/h = 8 hours.
3. Runner A has a 36 km head start and moves at 10 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?
3 hours
Relative closing speed = 22 − 10 = 12 km/h. Time = 36 km ÷ 12 km/h = 3 hours.
4. Runner A has a 18 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?
9 hours
Relative closing speed = 6 − 4 = 2 km/h. Time = 18 km ÷ 2 km/h = 9 hours.
5. Runner A has a 6 km head start and moves at 16 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?
2 hours
Relative closing speed = 19 − 16 = 3 km/h. Time = 6 km ÷ 3 km/h = 2 hours.
6. Runner A has a 33 km head start and moves at 12 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 − 12 = 11 km/h. Time = 33 km ÷ 11 km/h = 3 hours.
7. Runner A has a 50 km head start and moves at 18 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?
5 hours
Relative closing speed = 28 − 18 = 10 km/h. Time = 50 km ÷ 10 km/h = 5 hours.
8. Runner A has a 18 km head start and moves at 8 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?
6 hours
Relative closing speed = 11 − 8 = 3 km/h. Time = 18 km ÷ 3 km/h = 6 hours.
9. Runner A has a 28 km head start and moves at 9 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?
7 hours
Relative closing speed = 13 − 9 = 4 km/h. Time = 28 km ÷ 4 km/h = 7 hours.
10. Runner A has a 40 km head start and moves at 14 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?
8 hours
Relative closing speed = 19 − 14 = 5 km/h. Time = 40 km ÷ 5 km/h = 8 hours.
11. Runner A has a 24 km head start and moves at 7 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?
8 hours
Relative closing speed = 10 − 7 = 3 km/h. Time = 24 km ÷ 3 km/h = 8 hours.
12. 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.

12 questions · Seed 58 · Age guidance, not curriculum certification