ReasoningAges 10-12

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 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
4. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
8. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
10. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
11. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
12. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?

12 questions · Seed 52 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
126
The 7 machines produce 21 items per hour, so in 6 hours they produce 21 × 6 = 126 items.
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
693
The 7 machines produce 77 items per hour, so in 9 hours they produce 77 × 9 = 693 items.
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
252
The 2 machines produce 28 items per hour, so in 9 hours they produce 28 × 9 = 252 items.
4. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
528
The 6 machines produce 66 items per hour, so in 8 hours they produce 66 × 8 = 528 items.
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
360
The 3 machines produce 45 items per hour, so in 8 hours they produce 45 × 8 = 360 items.
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
48
The 4 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
588
The 7 machines produce 84 items per hour, so in 7 hours they produce 84 × 7 = 588 items.
8. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
490
The 7 machines produce 98 items per hour, so in 5 hours they produce 98 × 5 = 490 items.
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
441
The 7 machines produce 63 items per hour, so in 7 hours they produce 63 × 7 = 441 items.
10. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
280
The 4 machines produce 40 items per hour, so in 7 hours they produce 40 × 7 = 280 items.
11. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
294
The 7 machines produce 49 items per hour, so in 6 hours they produce 49 × 6 = 294 items.
12. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
120
The 5 machines produce 40 items per hour, so in 3 hours they produce 40 × 3 = 120 items.

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
4. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
8. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
10. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
11. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
12. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
126
The 7 machines produce 21 items per hour, so in 6 hours they produce 21 × 6 = 126 items.
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
693
The 7 machines produce 77 items per hour, so in 9 hours they produce 77 × 9 = 693 items.
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
252
The 2 machines produce 28 items per hour, so in 9 hours they produce 28 × 9 = 252 items.
4. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
528
The 6 machines produce 66 items per hour, so in 8 hours they produce 66 × 8 = 528 items.
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
360
The 3 machines produce 45 items per hour, so in 8 hours they produce 45 × 8 = 360 items.
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
48
The 4 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
588
The 7 machines produce 84 items per hour, so in 7 hours they produce 84 × 7 = 588 items.
8. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
490
The 7 machines produce 98 items per hour, so in 5 hours they produce 98 × 5 = 490 items.
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
441
The 7 machines produce 63 items per hour, so in 7 hours they produce 63 × 7 = 441 items.
10. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
280
The 4 machines produce 40 items per hour, so in 7 hours they produce 40 × 7 = 280 items.
11. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
294
The 7 machines produce 49 items per hour, so in 6 hours they produce 49 × 6 = 294 items.
12. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
120
The 5 machines produce 40 items per hour, so in 3 hours they produce 40 × 3 = 120 items.

12 questions · Seed 52 · Age guidance, not curriculum certification