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 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
2. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
3. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
4. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
5. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
6. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
7. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
8. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
9. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
10. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
11. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
12. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

12 questions · Seed 54 · 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 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
392
The 8 machines produce 56 items per hour, so in 7 hours they produce 56 × 7 = 392 items.
2. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
105
The 7 machines produce 21 items per hour, so in 5 hours they produce 21 × 5 = 105 items.
3. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
99
The 3 machines produce 33 items per hour, so in 3 hours they produce 33 × 3 = 99 items.
4. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
360
The 8 machines produce 72 items per hour, so in 5 hours they produce 72 × 5 = 360 items.
5. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
336
The 6 machines produce 42 items per hour, so in 8 hours they produce 42 × 8 = 336 items.
6. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
384
The 8 machines produce 48 items per hour, so in 8 hours they produce 48 × 8 = 384 items.
7. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
540
The 6 machines produce 90 items per hour, so in 6 hours they produce 90 × 6 = 540 items.
8. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
70
The 2 machines produce 14 items per hour, so in 5 hours they produce 14 × 5 = 70 items.
9. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
448
The 8 machines produce 56 items per hour, so in 8 hours they produce 56 × 8 = 448 items.
10. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
90
The 2 machines produce 10 items per hour, so in 9 hours they produce 10 × 9 = 90 items.
11. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
720
The 6 machines produce 90 items per hour, so in 8 hours they produce 90 × 8 = 720 items.
12. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
168
The 6 machines produce 24 items per hour, so in 7 hours they produce 24 × 7 = 168 items.

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
2. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
3. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
4. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
5. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
6. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
7. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
8. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
9. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
10. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
11. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
12. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?

12 questions · Seed 54 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
392
The 8 machines produce 56 items per hour, so in 7 hours they produce 56 × 7 = 392 items.
2. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
105
The 7 machines produce 21 items per hour, so in 5 hours they produce 21 × 5 = 105 items.
3. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
99
The 3 machines produce 33 items per hour, so in 3 hours they produce 33 × 3 = 99 items.
4. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
360
The 8 machines produce 72 items per hour, so in 5 hours they produce 72 × 5 = 360 items.
5. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
336
The 6 machines produce 42 items per hour, so in 8 hours they produce 42 × 8 = 336 items.
6. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
384
The 8 machines produce 48 items per hour, so in 8 hours they produce 48 × 8 = 384 items.
7. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
540
The 6 machines produce 90 items per hour, so in 6 hours they produce 90 × 6 = 540 items.
8. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
70
The 2 machines produce 14 items per hour, so in 5 hours they produce 14 × 5 = 70 items.
9. If 8 identical machines produce 56 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
448
The 8 machines produce 56 items per hour, so in 8 hours they produce 56 × 8 = 448 items.
10. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
90
The 2 machines produce 10 items per hour, so in 9 hours they produce 10 × 9 = 90 items.
11. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 8 hours at the same rate?
720
The 6 machines produce 90 items per hour, so in 8 hours they produce 90 × 8 = 720 items.
12. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
168
The 6 machines produce 24 items per hour, so in 7 hours they produce 24 × 7 = 168 items.

12 questions · Seed 54 · Age guidance, not curriculum certification