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 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
2. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
3. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 2 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 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
6. If 3 identical machines produce 15 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
7. If 8 identical machines produce 96 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
8. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
9. If 8 identical machines produce 40 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
10. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
11. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
12. If 3 identical machines produce 9 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?

12 questions · Seed 47 · 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. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
150
The 3 machines produce 30 items per hour, so in 5 hours they produce 30 × 5 = 150 items.
2. 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.
3. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
144
The 8 machines produce 72 items per hour, so in 2 hours they produce 72 × 2 = 144 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 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
420
The 6 machines produce 84 items per hour, so in 5 hours they produce 84 × 5 = 420 items.
6. If 3 identical machines produce 15 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
135
The 3 machines produce 15 items per hour, so in 9 hours they produce 15 × 9 = 135 items.
7. If 8 identical machines produce 96 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
864
The 8 machines produce 96 items per hour, so in 9 hours they produce 96 × 9 = 864 items.
8. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
20
The 2 machines produce 10 items per hour, so in 2 hours they produce 10 × 2 = 20 items.
9. If 8 identical machines produce 40 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
360
The 8 machines produce 40 items per hour, so in 9 hours they produce 40 × 9 = 360 items.
10. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
396
The 6 machines produce 66 items per hour, so in 6 hours they produce 66 × 6 = 396 items.
11. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
315
The 5 machines produce 35 items per hour, so in 9 hours they produce 35 × 9 = 315 items.
12. If 3 identical machines produce 9 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
54
The 3 machines produce 9 items per hour, so in 6 hours they produce 9 × 6 = 54 items.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
2. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
3. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 2 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 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
6. If 3 identical machines produce 15 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
7. If 8 identical machines produce 96 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
8. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
9. If 8 identical machines produce 40 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
10. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
11. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
12. If 3 identical machines produce 9 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
150
The 3 machines produce 30 items per hour, so in 5 hours they produce 30 × 5 = 150 items.
2. 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.
3. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 2 hours at the same rate?
144
The 8 machines produce 72 items per hour, so in 2 hours they produce 72 × 2 = 144 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 6 identical machines produce 84 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
420
The 6 machines produce 84 items per hour, so in 5 hours they produce 84 × 5 = 420 items.
6. If 3 identical machines produce 15 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
135
The 3 machines produce 15 items per hour, so in 9 hours they produce 15 × 9 = 135 items.
7. If 8 identical machines produce 96 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
864
The 8 machines produce 96 items per hour, so in 9 hours they produce 96 × 9 = 864 items.
8. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
20
The 2 machines produce 10 items per hour, so in 2 hours they produce 10 × 2 = 20 items.
9. If 8 identical machines produce 40 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
360
The 8 machines produce 40 items per hour, so in 9 hours they produce 40 × 9 = 360 items.
10. If 6 identical machines produce 66 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
396
The 6 machines produce 66 items per hour, so in 6 hours they produce 66 × 6 = 396 items.
11. If 5 identical machines produce 35 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
315
The 5 machines produce 35 items per hour, so in 9 hours they produce 35 × 9 = 315 items.
12. If 3 identical machines produce 9 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
54
The 3 machines produce 9 items per hour, so in 6 hours they produce 9 × 6 = 54 items.

12 questions · Seed 47 · Age guidance, not curriculum certification