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 16 km head start and moves at 5 km/h. Runner B chases in the same direction at 7 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 49 km head start and moves at 18 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?
3. Runner A has a 22 km head start and moves at 10 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?
4. Runner A has a 72 km head start and moves at 16 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?
5. Runner A has a 99 km head start and moves at 11 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?
6. Runner A has a 77 km head start and moves at 15 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?
7. Runner A has a 30 km head start and moves at 7 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?
8. Runner A has a 21 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?
9. Runner A has a 70 km head start and moves at 7 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?
10. Runner A has a 30 km head start and moves at 18 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?
11. Runner A has a 108 km head start and moves at 6 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 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?

12 questions · Seed 104731 · 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 16 km head start and moves at 5 km/h. Runner B chases in the same direction at 7 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 7 − 5 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.
2. Runner A has a 49 km head start and moves at 18 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?
7 hours
Relative closing speed = 25 − 18 = 7 km/h. Time = 49 km ÷ 7 km/h = 7 hours.
3. Runner A has a 22 km head start and moves at 10 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 − 10 = 11 km/h. Time = 22 km ÷ 11 km/h = 2 hours.
4. Runner A has a 72 km head start and moves at 16 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?
9 hours
Relative closing speed = 24 − 16 = 8 km/h. Time = 72 km ÷ 8 km/h = 9 hours.
5. Runner A has a 99 km head start and moves at 11 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 − 11 = 11 km/h. Time = 99 km ÷ 11 km/h = 9 hours.
6. Runner A has a 77 km head start and moves at 15 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?
7 hours
Relative closing speed = 26 − 15 = 11 km/h. Time = 77 km ÷ 11 km/h = 7 hours.
7. Runner A has a 30 km head start and moves at 7 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 − 7 = 10 km/h. Time = 30 km ÷ 10 km/h = 3 hours.
8. Runner A has a 21 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 hours
Relative closing speed = 18 − 11 = 7 km/h. Time = 21 km ÷ 7 km/h = 3 hours.
9. Runner A has a 70 km head start and moves at 7 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?
7 hours
Relative closing speed = 17 − 7 = 10 km/h. Time = 70 km ÷ 10 km/h = 7 hours.
10. Runner A has a 30 km head start and moves at 18 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?
6 hours
Relative closing speed = 23 − 18 = 5 km/h. Time = 30 km ÷ 5 km/h = 6 hours.
11. Runner A has a 108 km head start and moves at 6 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 − 6 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.
12. Runner A has a 72 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?
6 hours
Relative closing speed = 19 − 7 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

12 questions · Seed 104731 · 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 16 km head start and moves at 5 km/h. Runner B chases in the same direction at 7 km/h. How many hours will it take Runner B to catch Runner A?
2. Runner A has a 49 km head start and moves at 18 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?
3. Runner A has a 22 km head start and moves at 10 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?
4. Runner A has a 72 km head start and moves at 16 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?
5. Runner A has a 99 km head start and moves at 11 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?
6. Runner A has a 77 km head start and moves at 15 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?
7. Runner A has a 30 km head start and moves at 7 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?
8. Runner A has a 21 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?
9. Runner A has a 70 km head start and moves at 7 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?
10. Runner A has a 30 km head start and moves at 18 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?
11. Runner A has a 108 km head start and moves at 6 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 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?

12 questions · Seed 104731 · 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 16 km head start and moves at 5 km/h. Runner B chases in the same direction at 7 km/h. How many hours will it take Runner B to catch Runner A?
8 hours
Relative closing speed = 7 − 5 = 2 km/h. Time = 16 km ÷ 2 km/h = 8 hours.
2. Runner A has a 49 km head start and moves at 18 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?
7 hours
Relative closing speed = 25 − 18 = 7 km/h. Time = 49 km ÷ 7 km/h = 7 hours.
3. Runner A has a 22 km head start and moves at 10 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 − 10 = 11 km/h. Time = 22 km ÷ 11 km/h = 2 hours.
4. Runner A has a 72 km head start and moves at 16 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?
9 hours
Relative closing speed = 24 − 16 = 8 km/h. Time = 72 km ÷ 8 km/h = 9 hours.
5. Runner A has a 99 km head start and moves at 11 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 − 11 = 11 km/h. Time = 99 km ÷ 11 km/h = 9 hours.
6. Runner A has a 77 km head start and moves at 15 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?
7 hours
Relative closing speed = 26 − 15 = 11 km/h. Time = 77 km ÷ 11 km/h = 7 hours.
7. Runner A has a 30 km head start and moves at 7 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 − 7 = 10 km/h. Time = 30 km ÷ 10 km/h = 3 hours.
8. Runner A has a 21 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 hours
Relative closing speed = 18 − 11 = 7 km/h. Time = 21 km ÷ 7 km/h = 3 hours.
9. Runner A has a 70 km head start and moves at 7 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?
7 hours
Relative closing speed = 17 − 7 = 10 km/h. Time = 70 km ÷ 10 km/h = 7 hours.
10. Runner A has a 30 km head start and moves at 18 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?
6 hours
Relative closing speed = 23 − 18 = 5 km/h. Time = 30 km ÷ 5 km/h = 6 hours.
11. Runner A has a 108 km head start and moves at 6 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 − 6 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.
12. Runner A has a 72 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?
6 hours
Relative closing speed = 19 − 7 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

12 questions · Seed 104731 · Age guidance, not curriculum certification