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 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
2. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
4. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
5. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
6. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?
7. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
9. If 5 identical machines produce 30 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
10. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
11. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
12. If 7 identical machines produce 35 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?

12 questions · Seed 44 · 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 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
280
The 5 machines produce 40 items per hour, so in 7 hours they produce 40 × 7 = 280 items.
2. 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.
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
252
The 6 machines produce 42 items per hour, so in 6 hours they produce 42 × 6 = 252 items.
4. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
784
The 7 machines produce 98 items per hour, so in 8 hours they produce 98 × 8 = 784 items.
5. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
378
The 6 machines produce 54 items per hour, so in 7 hours they produce 54 × 7 = 378 items.
6. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?
108
The 6 machines produce 36 items per hour, so in 3 hours they produce 36 × 3 = 108 items.
7. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
60
The 2 machines produce 20 items per hour, so in 3 hours they produce 20 × 3 = 60 items.
8. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
60
The 3 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
9. If 5 identical machines produce 30 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
120
The 5 machines produce 30 items per hour, so in 4 hours they produce 30 × 4 = 120 items.
10. 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.
11. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
75
The 5 machines produce 25 items per hour, so in 3 hours they produce 25 × 3 = 75 items.
12. If 7 identical machines produce 35 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
175
The 7 machines produce 35 items per hour, so in 5 hours they produce 35 × 5 = 175 items.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
2. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
4. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
5. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
6. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?
7. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
9. If 5 identical machines produce 30 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
10. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
11. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
12. If 7 identical machines produce 35 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 5 identical machines produce 40 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
280
The 5 machines produce 40 items per hour, so in 7 hours they produce 40 × 7 = 280 items.
2. 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.
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
252
The 6 machines produce 42 items per hour, so in 6 hours they produce 42 × 6 = 252 items.
4. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
784
The 7 machines produce 98 items per hour, so in 8 hours they produce 98 × 8 = 784 items.
5. If 6 identical machines produce 54 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
378
The 6 machines produce 54 items per hour, so in 7 hours they produce 54 × 7 = 378 items.
6. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 3 hours at the same rate?
108
The 6 machines produce 36 items per hour, so in 3 hours they produce 36 × 3 = 108 items.
7. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
60
The 2 machines produce 20 items per hour, so in 3 hours they produce 20 × 3 = 60 items.
8. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
60
The 3 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
9. If 5 identical machines produce 30 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
120
The 5 machines produce 30 items per hour, so in 4 hours they produce 30 × 4 = 120 items.
10. 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.
11. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
75
The 5 machines produce 25 items per hour, so in 3 hours they produce 25 × 3 = 75 items.
12. If 7 identical machines produce 35 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
175
The 7 machines produce 35 items per hour, so in 5 hours they produce 35 × 5 = 175 items.

12 questions · Seed 44 · Age guidance, not curriculum certification