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ReasoningAges 13-15

Combined work-rate puzzles

Add two individual work rates together to find how long two machines take to complete a shared job. 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

Combined work-rate puzzles

Take your time. Show your thinking.

  1. 1. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?

    3+3942+391+393+39?

  2. 2. If 6 identical machines produce 78 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?

    6+7278+721+726+72?

  3. 3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?

    2+2426+241+242+24?

  4. 4. If 2 identical machines produce 6 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

    2+46+41+42+4?

  5. 5. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    6+6672+661+666+66?

  6. 6. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    6+4854+481+486+48?

  7. 7. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

    6+6066+601+606+60?

  8. 8. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

    2+1416+141+142+14?

  9. 9. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 3 hours at the same rate?

    7+1421+141+147+14?

  10. 10. If 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?

    6+7884+781+786+78?

  11. 11. If 8 identical machines produce 120 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

    8+112120+1121+1128+112?

  12. 12. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?

    3+912+91+93+9?
12 questions · Seed 51 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

  1. 1. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?

    168

    The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.

  2. 2. If 6 identical machines produce 78 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?

    234

    The 6 machines produce 78 items per hour, so in 3 hours they produce 78 × 3 = 234 items.

  3. 3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?

    52

    The 2 machines produce 26 items per hour, so in 2 hours they produce 26 × 2 = 52 items.

  4. 4. If 2 identical machines produce 6 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

    48

    The 2 machines produce 6 items per hour, so in 8 hours they produce 6 × 8 = 48 items.

  5. 5. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    288

    The 6 machines produce 72 items per hour, so in 4 hours they produce 72 × 4 = 288 items.

  6. 6. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    216

    The 6 machines produce 54 items per hour, so in 4 hours they produce 54 × 4 = 216 items.

  7. 7. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

    462

    The 6 machines produce 66 items per hour, so in 7 hours they produce 66 × 7 = 462 items.

  8. 8. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

    96

    The 2 machines produce 16 items per hour, so in 6 hours they produce 16 × 6 = 96 items.

  9. 9. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 3 hours at the same rate?

    63

    The 7 machines produce 21 items per hour, so in 3 hours they produce 21 × 3 = 63 items.

  10. 10. If 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?

    168

    The 6 machines produce 84 items per hour, so in 2 hours they produce 84 × 2 = 168 items.

  11. 11. If 8 identical machines produce 120 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

    960

    The 8 machines produce 120 items per hour, so in 8 hours they produce 120 × 8 = 960 items.

  12. 12. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?

    84

    The 3 machines produce 12 items per hour, so in 7 hours they produce 12 × 7 = 84 items.

12 questions · Seed 51 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

  1. 1. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?

    3+3942+391+393+39?

  2. 2. If 6 identical machines produce 78 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?

    6+7278+721+726+72?

  3. 3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?

    2+2426+241+242+24?

  4. 4. If 2 identical machines produce 6 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

    2+46+41+42+4?

  5. 5. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    6+6672+661+666+66?

  6. 6. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    6+4854+481+486+48?

  7. 7. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

    6+6066+601+606+60?

  8. 8. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

    2+1416+141+142+14?

  9. 9. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 3 hours at the same rate?

    7+1421+141+147+14?

  10. 10. If 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?

    6+7884+781+786+78?

  11. 11. If 8 identical machines produce 120 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

    8+112120+1121+1128+112?

  12. 12. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?

    3+912+91+93+9?
12 questions · Seed 51 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

  1. 1. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?

    168

    The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.

  2. 2. If 6 identical machines produce 78 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?

    234

    The 6 machines produce 78 items per hour, so in 3 hours they produce 78 × 3 = 234 items.

  3. 3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?

    52

    The 2 machines produce 26 items per hour, so in 2 hours they produce 26 × 2 = 52 items.

  4. 4. If 2 identical machines produce 6 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

    48

    The 2 machines produce 6 items per hour, so in 8 hours they produce 6 × 8 = 48 items.

  5. 5. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    288

    The 6 machines produce 72 items per hour, so in 4 hours they produce 72 × 4 = 288 items.

  6. 6. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

    216

    The 6 machines produce 54 items per hour, so in 4 hours they produce 54 × 4 = 216 items.

  7. 7. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

    462

    The 6 machines produce 66 items per hour, so in 7 hours they produce 66 × 7 = 462 items.

  8. 8. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

    96

    The 2 machines produce 16 items per hour, so in 6 hours they produce 16 × 6 = 96 items.

  9. 9. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 3 hours at the same rate?

    63

    The 7 machines produce 21 items per hour, so in 3 hours they produce 21 × 3 = 63 items.

  10. 10. If 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?

    168

    The 6 machines produce 84 items per hour, so in 2 hours they produce 84 × 2 = 168 items.

  11. 11. If 8 identical machines produce 120 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

    960

    The 8 machines produce 120 items per hour, so in 8 hours they produce 120 × 8 = 960 items.

  12. 12. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?

    84

    The 3 machines produce 12 items per hour, so in 7 hours they produce 12 × 7 = 84 items.

12 questions · Seed 51 · Age guidance, not curriculum certification