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 88 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
2. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
3. If 4 identical machines produce 28 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
4. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
5. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
7. If 4 identical machines produce 12 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
8. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
9. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
10. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
11. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
12. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?

12 questions · Seed 49 · 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 88 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
528
The 8 machines produce 88 items per hour, so in 6 hours they produce 88 × 6 = 528 items.
2. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
245
The 7 machines produce 49 items per hour, so in 5 hours they produce 49 × 5 = 245 items.
3. If 4 identical machines produce 28 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
140
The 4 machines produce 28 items per hour, so in 5 hours they produce 28 × 5 = 140 items.
4. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
130
The 5 machines produce 65 items per hour, so in 2 hours they produce 65 × 2 = 130 items.
5. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
882
The 7 machines produce 98 items per hour, so in 9 hours they produce 98 × 9 = 882 items.
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
64
The 2 machines produce 16 items per hour, so in 4 hours they produce 16 × 4 = 64 items.
7. If 4 identical machines produce 12 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
60
The 4 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
8. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
198
The 2 machines produce 22 items per hour, so in 9 hours they produce 22 × 9 = 198 items.
9. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
80
The 2 machines produce 16 items per hour, so in 5 hours they produce 16 × 5 = 80 items.
10. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
160
The 8 machines produce 80 items per hour, so in 2 hours they produce 80 × 2 = 160 items.
11. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
336
The 4 machines produce 56 items per hour, so in 6 hours they produce 56 × 6 = 336 items.
12. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
140
The 5 machines produce 35 items per hour, so in 4 hours they produce 35 × 4 = 140 items.

12 questions · Seed 49 · 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 88 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
2. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
3. If 4 identical machines produce 28 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
4. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
5. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
7. If 4 identical machines produce 12 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
8. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
9. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
10. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
11. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
12. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?

12 questions · Seed 49 · 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 88 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
528
The 8 machines produce 88 items per hour, so in 6 hours they produce 88 × 6 = 528 items.
2. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
245
The 7 machines produce 49 items per hour, so in 5 hours they produce 49 × 5 = 245 items.
3. If 4 identical machines produce 28 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
140
The 4 machines produce 28 items per hour, so in 5 hours they produce 28 × 5 = 140 items.
4. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
130
The 5 machines produce 65 items per hour, so in 2 hours they produce 65 × 2 = 130 items.
5. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
882
The 7 machines produce 98 items per hour, so in 9 hours they produce 98 × 9 = 882 items.
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
64
The 2 machines produce 16 items per hour, so in 4 hours they produce 16 × 4 = 64 items.
7. If 4 identical machines produce 12 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
60
The 4 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
8. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
198
The 2 machines produce 22 items per hour, so in 9 hours they produce 22 × 9 = 198 items.
9. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
80
The 2 machines produce 16 items per hour, so in 5 hours they produce 16 × 5 = 80 items.
10. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
160
The 8 machines produce 80 items per hour, so in 2 hours they produce 80 × 2 = 160 items.
11. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
336
The 4 machines produce 56 items per hour, so in 6 hours they produce 56 × 6 = 336 items.
12. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
140
The 5 machines produce 35 items per hour, so in 4 hours they produce 35 × 4 = 140 items.

12 questions · Seed 49 · Age guidance, not curriculum certification