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 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
3. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
4. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
8. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
9. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
10. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
11. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
12. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

12 questions · Seed 104731 · 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 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
24
The 2 machines produce 12 items per hour, so in 2 hours they produce 12 × 2 = 24 items.
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
270
The 3 machines produce 45 items per hour, so in 6 hours they produce 45 × 6 = 270 items.
3. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
252
The 7 machines produce 63 items per hour, so in 4 hours they produce 63 × 4 = 252 items.
4. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
90
The 3 machines produce 30 items per hour, so in 3 hours they produce 30 × 3 = 90 items.
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
256
The 4 machines produce 32 items per hour, so in 8 hours they produce 32 × 8 = 256 items.
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
112
The 2 machines produce 16 items per hour, so in 7 hours they produce 16 × 7 = 112 items.
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
672
The 7 machines produce 84 items per hour, so in 8 hours they produce 84 × 8 = 672 items.
8. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
154
The 7 machines produce 77 items per hour, so in 2 hours they produce 77 × 2 = 154 items.
9. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
225
The 3 machines produce 45 items per hour, so in 5 hours they produce 45 × 5 = 225 items.
10. 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.
11. 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.
12. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
144
The 2 machines produce 24 items per hour, so in 6 hours they produce 24 × 6 = 144 items.

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
3. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
4. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
8. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
9. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
10. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
11. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
12. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?

12 questions · Seed 104731 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
24
The 2 machines produce 12 items per hour, so in 2 hours they produce 12 × 2 = 24 items.
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
270
The 3 machines produce 45 items per hour, so in 6 hours they produce 45 × 6 = 270 items.
3. If 7 identical machines produce 63 items in 1 hour, how many items will 7 machines produce in 4 hours at the same rate?
252
The 7 machines produce 63 items per hour, so in 4 hours they produce 63 × 4 = 252 items.
4. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
90
The 3 machines produce 30 items per hour, so in 3 hours they produce 30 × 3 = 90 items.
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
256
The 4 machines produce 32 items per hour, so in 8 hours they produce 32 × 8 = 256 items.
6. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
112
The 2 machines produce 16 items per hour, so in 7 hours they produce 16 × 7 = 112 items.
7. If 7 identical machines produce 84 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
672
The 7 machines produce 84 items per hour, so in 8 hours they produce 84 × 8 = 672 items.
8. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
154
The 7 machines produce 77 items per hour, so in 2 hours they produce 77 × 2 = 154 items.
9. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
225
The 3 machines produce 45 items per hour, so in 5 hours they produce 45 × 5 = 225 items.
10. 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.
11. 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.
12. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
144
The 2 machines produce 24 items per hour, so in 6 hours they produce 24 × 6 = 144 items.

12 questions · Seed 104731 · Age guidance, not curriculum certification