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 48 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
2. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
3. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
5. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
6. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
7. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
10. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
11. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 3 hours at the same rate?

12 questions · Seed 48 · 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 48 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
240
The 8 machines produce 48 items per hour, so in 5 hours they produce 48 × 5 = 240 items.
2. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
100
The 5 machines produce 50 items per hour, so in 2 hours they produce 50 × 2 = 100 items.
3. 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.
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
324
The 3 machines produce 36 items per hour, so in 9 hours they produce 36 × 9 = 324 items.
5. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
336
The 7 machines produce 84 items per hour, so in 4 hours they produce 84 × 4 = 336 items.
6. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
110
The 5 machines produce 55 items per hour, so in 2 hours they produce 55 × 2 = 110 items.
7. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
325
The 5 machines produce 65 items per hour, so in 5 hours they produce 65 × 5 = 325 items.
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
384
The 8 machines produce 64 items per hour, so in 6 hours they produce 64 × 6 = 384 items.
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
504
The 7 machines produce 63 items per hour, so in 8 hours they produce 63 × 8 = 504 items.
10. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
130
The 2 machines produce 26 items per hour, so in 5 hours they produce 26 × 5 = 130 items.
11. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
108
The 3 machines produce 12 items per hour, so in 9 hours they produce 12 × 9 = 108 items.
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 3 hours at the same rate?
240
The 8 machines produce 80 items per hour, so in 3 hours they produce 80 × 3 = 240 items.

12 questions · Seed 48 · 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 48 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
2. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
3. If 7 identical machines produce 49 items in 1 hour, how many items will 7 machines produce in 6 hours at the same rate?
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
5. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
6. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
7. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
10. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
11. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 3 hours at the same rate?

12 questions · Seed 48 · 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 48 items in 1 hour, how many items will 8 machines produce in 5 hours at the same rate?
240
The 8 machines produce 48 items per hour, so in 5 hours they produce 48 × 5 = 240 items.
2. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
100
The 5 machines produce 50 items per hour, so in 2 hours they produce 50 × 2 = 100 items.
3. 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.
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
324
The 3 machines produce 36 items per hour, so in 9 hours they produce 36 × 9 = 324 items.
5. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
336
The 7 machines produce 84 items per hour, so in 4 hours they produce 84 × 4 = 336 items.
6. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
110
The 5 machines produce 55 items per hour, so in 2 hours they produce 55 × 2 = 110 items.
7. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
325
The 5 machines produce 65 items per hour, so in 5 hours they produce 65 × 5 = 325 items.
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
384
The 8 machines produce 64 items per hour, so in 6 hours they produce 64 × 6 = 384 items.
9. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
504
The 7 machines produce 63 items per hour, so in 8 hours they produce 63 × 8 = 504 items.
10. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
130
The 2 machines produce 26 items per hour, so in 5 hours they produce 26 × 5 = 130 items.
11. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
108
The 3 machines produce 12 items per hour, so in 9 hours they produce 12 × 9 = 108 items.
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 3 hours at the same rate?
240
The 8 machines produce 80 items per hour, so in 3 hours they produce 80 × 3 = 240 items.

12 questions · Seed 48 · Age guidance, not curriculum certification