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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 10-12Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Relative speed & pursuit puzzles

Take your time. Show your thinking.

  1. 1. Runner A has a 12 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?

    12-57-513-5?

  2. 2. Runner A has a 42 km head start and moves at 9 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?

    42-339-3316-33?

  3. 3. Runner A has a 15 km head start and moves at 6 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?

    15-96-911-9?

  4. 4. Runner A has a 72 km head start and moves at 9 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?

    72-639-6321-63?

  5. 5. Runner A has a 18 km head start and moves at 16 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?

    18-216-222-2?

  6. 6. Runner A has a 10 km head start and moves at 15 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+515+517+5?

  7. 7. Runner A has a 72 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?

    72-6210-6222-62?

  8. 8. Runner A has a 21 km head start and moves at 17 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?

    21-417-420-4?

  9. 9. Runner A has a 8 km head start and moves at 7 km/h. Runner B chases in the same direction at 9 km/h. How many hours will it take Runner B to catch Runner A?

    8-17-19-1?

  10. 10. Runner A has a 81 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?

    81-747-7416-74?

  11. 11. Runner A has a 10 km head start and moves at 8 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?

    10-28-210-2?

  12. 12. Runner A has a 40 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?

    40-2416-2421-24?
12 questions · Seed 48 · 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. 1. Runner A has a 12 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?

    2 hours

    Relative closing speed = 13 − 7 = 6 km/h. Time = 12 km ÷ 6 km/h = 2 hours.

  2. 2. Runner A has a 42 km head start and moves at 9 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?

    6 hours

    Relative closing speed = 16 − 9 = 7 km/h. Time = 42 km ÷ 7 km/h = 6 hours.

  3. 3. Runner A has a 15 km head start and moves at 6 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?

    3 hours

    Relative closing speed = 11 − 6 = 5 km/h. Time = 15 km ÷ 5 km/h = 3 hours.

  4. 4. Runner A has a 72 km head start and moves at 9 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?

    6 hours

    Relative closing speed = 21 − 9 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

  5. 5. Runner A has a 18 km head start and moves at 16 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 − 16 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.

  6. 6. Runner A has a 10 km head start and moves at 15 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?

    5 hours

    Relative closing speed = 17 − 15 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.

  7. 7. Runner A has a 72 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?

    6 hours

    Relative closing speed = 22 − 10 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

  8. 8. Runner A has a 21 km head start and moves at 17 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?

    7 hours

    Relative closing speed = 20 − 17 = 3 km/h. Time = 21 km ÷ 3 km/h = 7 hours.

  9. 9. Runner A has a 8 km head start and moves at 7 km/h. Runner B chases in the same direction at 9 km/h. How many hours will it take Runner B to catch Runner A?

    4 hours

    Relative closing speed = 9 − 7 = 2 km/h. Time = 8 km ÷ 2 km/h = 4 hours.

  10. 10. Runner A has a 81 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?

    9 hours

    Relative closing speed = 16 − 7 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.

  11. 11. Runner A has a 10 km head start and moves at 8 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?

    5 hours

    Relative closing speed = 10 − 8 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.

  12. 12. Runner A has a 40 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?

    8 hours

    Relative closing speed = 21 − 16 = 5 km/h. Time = 40 km ÷ 5 km/h = 8 hours.

12 questions · Seed 48 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 10-12

Relative speed & pursuit puzzles

Take your time. Show your thinking.

  1. 1. Runner A has a 12 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?

    12-57-513-5?

  2. 2. Runner A has a 42 km head start and moves at 9 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?

    42-339-3316-33?

  3. 3. Runner A has a 15 km head start and moves at 6 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?

    15-96-911-9?

  4. 4. Runner A has a 72 km head start and moves at 9 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?

    72-639-6321-63?

  5. 5. Runner A has a 18 km head start and moves at 16 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?

    18-216-222-2?

  6. 6. Runner A has a 10 km head start and moves at 15 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+515+517+5?

  7. 7. Runner A has a 72 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?

    72-6210-6222-62?

  8. 8. Runner A has a 21 km head start and moves at 17 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?

    21-417-420-4?

  9. 9. Runner A has a 8 km head start and moves at 7 km/h. Runner B chases in the same direction at 9 km/h. How many hours will it take Runner B to catch Runner A?

    8-17-19-1?

  10. 10. Runner A has a 81 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?

    81-747-7416-74?

  11. 11. Runner A has a 10 km head start and moves at 8 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?

    10-28-210-2?

  12. 12. Runner A has a 40 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?

    40-2416-2421-24?
12 questions · Seed 48 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 10-12

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

  1. 1. Runner A has a 12 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?

    2 hours

    Relative closing speed = 13 − 7 = 6 km/h. Time = 12 km ÷ 6 km/h = 2 hours.

  2. 2. Runner A has a 42 km head start and moves at 9 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?

    6 hours

    Relative closing speed = 16 − 9 = 7 km/h. Time = 42 km ÷ 7 km/h = 6 hours.

  3. 3. Runner A has a 15 km head start and moves at 6 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?

    3 hours

    Relative closing speed = 11 − 6 = 5 km/h. Time = 15 km ÷ 5 km/h = 3 hours.

  4. 4. Runner A has a 72 km head start and moves at 9 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?

    6 hours

    Relative closing speed = 21 − 9 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

  5. 5. Runner A has a 18 km head start and moves at 16 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 − 16 = 6 km/h. Time = 18 km ÷ 6 km/h = 3 hours.

  6. 6. Runner A has a 10 km head start and moves at 15 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?

    5 hours

    Relative closing speed = 17 − 15 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.

  7. 7. Runner A has a 72 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?

    6 hours

    Relative closing speed = 22 − 10 = 12 km/h. Time = 72 km ÷ 12 km/h = 6 hours.

  8. 8. Runner A has a 21 km head start and moves at 17 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?

    7 hours

    Relative closing speed = 20 − 17 = 3 km/h. Time = 21 km ÷ 3 km/h = 7 hours.

  9. 9. Runner A has a 8 km head start and moves at 7 km/h. Runner B chases in the same direction at 9 km/h. How many hours will it take Runner B to catch Runner A?

    4 hours

    Relative closing speed = 9 − 7 = 2 km/h. Time = 8 km ÷ 2 km/h = 4 hours.

  10. 10. Runner A has a 81 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?

    9 hours

    Relative closing speed = 16 − 7 = 9 km/h. Time = 81 km ÷ 9 km/h = 9 hours.

  11. 11. Runner A has a 10 km head start and moves at 8 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?

    5 hours

    Relative closing speed = 10 − 8 = 2 km/h. Time = 10 km ÷ 2 km/h = 5 hours.

  12. 12. Runner A has a 40 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?

    8 hours

    Relative closing speed = 21 − 16 = 5 km/h. Time = 40 km ÷ 5 km/h = 8 hours.

12 questions · Seed 48 · Age guidance, not curriculum certification