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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 10-12Ages 13-15

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Worksheet StudioPractice pack · Ages 13-15

Relative speed & pursuit puzzles

Take your time. Show your thinking.

  1. 1. Runner A has a 24 km head start and moves at 5 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?

    24-195-1911-19?

  2. 2. Runner A has a 24 km head start and moves at 5 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?

    24-195-1913-19?

  3. 3. Runner A has a 18 km head start and moves at 17 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?

    18-117-126-1?

  4. 4. Runner A has a 66 km head start and moves at 14 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?

    66-5214-5225-52?

  5. 5. Runner A has a 96 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?

    96-897-8919-89?

  6. 6. Runner A has a 108 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?

    108-1008-10020-100?

  7. 7. Runner A has a 45 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?

    45-3312-3321-33?

  8. 8. Runner A has a 60 km head start and moves at 11 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?

    60-4911-4921-49?

  9. 9. Runner A has a 16 km head start and moves at 4 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?

    16-124-1212-12?

  10. 10. 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?

  11. 11. Runner A has a 9 km head start and moves at 15 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+615+618+6?

  12. 12. Runner A has a 48 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?

    48-3810-3822-38?
12 questions · Seed 45 · 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. 1. Runner A has a 24 km head start and moves at 5 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?

    4 hours

    Relative closing speed = 11 − 5 = 6 km/h. Time = 24 km ÷ 6 km/h = 4 hours.

  2. 2. Runner A has a 24 km head start and moves at 5 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?

    3 hours

    Relative closing speed = 13 − 5 = 8 km/h. Time = 24 km ÷ 8 km/h = 3 hours.

  3. 3. Runner A has a 18 km head start and moves at 17 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?

    2 hours

    Relative closing speed = 26 − 17 = 9 km/h. Time = 18 km ÷ 9 km/h = 2 hours.

  4. 4. Runner A has a 66 km head start and moves at 14 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?

    6 hours

    Relative closing speed = 25 − 14 = 11 km/h. Time = 66 km ÷ 11 km/h = 6 hours.

  5. 5. Runner A has a 96 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?

    8 hours

    Relative closing speed = 19 − 7 = 12 km/h. Time = 96 km ÷ 12 km/h = 8 hours.

  6. 6. Runner A has a 108 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?

    9 hours

    Relative closing speed = 20 − 8 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.

  7. 7. Runner A has a 45 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?

    5 hours

    Relative closing speed = 21 − 12 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.

  8. 8. Runner A has a 60 km head start and moves at 11 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 − 11 = 10 km/h. Time = 60 km ÷ 10 km/h = 6 hours.

  9. 9. Runner A has a 16 km head start and moves at 4 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?

    2 hours

    Relative closing speed = 12 − 4 = 8 km/h. Time = 16 km ÷ 8 km/h = 2 hours.

  10. 10. 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.

  11. 11. Runner A has a 9 km head start and moves at 15 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 − 15 = 3 km/h. Time = 9 km ÷ 3 km/h = 3 hours.

  12. 12. Runner A has a 48 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 hours

    Relative closing speed = 22 − 10 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.

12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Relative speed & pursuit puzzles

Take your time. Show your thinking.

  1. 1. Runner A has a 24 km head start and moves at 5 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?

    24-195-1911-19?

  2. 2. Runner A has a 24 km head start and moves at 5 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?

    24-195-1913-19?

  3. 3. Runner A has a 18 km head start and moves at 17 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?

    18-117-126-1?

  4. 4. Runner A has a 66 km head start and moves at 14 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?

    66-5214-5225-52?

  5. 5. Runner A has a 96 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?

    96-897-8919-89?

  6. 6. Runner A has a 108 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?

    108-1008-10020-100?

  7. 7. Runner A has a 45 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?

    45-3312-3321-33?

  8. 8. Runner A has a 60 km head start and moves at 11 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?

    60-4911-4921-49?

  9. 9. Runner A has a 16 km head start and moves at 4 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?

    16-124-1212-12?

  10. 10. 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?

  11. 11. Runner A has a 9 km head start and moves at 15 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+615+618+6?

  12. 12. Runner A has a 48 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?

    48-3810-3822-38?
12 questions · Seed 45 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Relative speed & pursuit puzzles

Answers and reasoning. Review before teaching.

  1. 1. Runner A has a 24 km head start and moves at 5 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?

    4 hours

    Relative closing speed = 11 − 5 = 6 km/h. Time = 24 km ÷ 6 km/h = 4 hours.

  2. 2. Runner A has a 24 km head start and moves at 5 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?

    3 hours

    Relative closing speed = 13 − 5 = 8 km/h. Time = 24 km ÷ 8 km/h = 3 hours.

  3. 3. Runner A has a 18 km head start and moves at 17 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?

    2 hours

    Relative closing speed = 26 − 17 = 9 km/h. Time = 18 km ÷ 9 km/h = 2 hours.

  4. 4. Runner A has a 66 km head start and moves at 14 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?

    6 hours

    Relative closing speed = 25 − 14 = 11 km/h. Time = 66 km ÷ 11 km/h = 6 hours.

  5. 5. Runner A has a 96 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?

    8 hours

    Relative closing speed = 19 − 7 = 12 km/h. Time = 96 km ÷ 12 km/h = 8 hours.

  6. 6. Runner A has a 108 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?

    9 hours

    Relative closing speed = 20 − 8 = 12 km/h. Time = 108 km ÷ 12 km/h = 9 hours.

  7. 7. Runner A has a 45 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?

    5 hours

    Relative closing speed = 21 − 12 = 9 km/h. Time = 45 km ÷ 9 km/h = 5 hours.

  8. 8. Runner A has a 60 km head start and moves at 11 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 − 11 = 10 km/h. Time = 60 km ÷ 10 km/h = 6 hours.

  9. 9. Runner A has a 16 km head start and moves at 4 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?

    2 hours

    Relative closing speed = 12 − 4 = 8 km/h. Time = 16 km ÷ 8 km/h = 2 hours.

  10. 10. 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.

  11. 11. Runner A has a 9 km head start and moves at 15 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 − 15 = 3 km/h. Time = 9 km ÷ 3 km/h = 3 hours.

  12. 12. Runner A has a 48 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 hours

    Relative closing speed = 22 − 10 = 12 km/h. Time = 48 km ÷ 12 km/h = 4 hours.

12 questions · Seed 45 · Age guidance, not curriculum certification