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 30 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
2. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
3. If 7 identical machines produce 70 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
4. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
6. If 3 identical machines produce 39 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
7. If 4 identical machines produce 36 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
8. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
9. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
10. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
12. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

12 questions · Seed 42 · 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 30 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
90
The 2 machines produce 30 items per hour, so in 3 hours they produce 30 × 3 = 90 items.
2. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
160
The 4 machines produce 20 items per hour, so in 8 hours they produce 20 × 8 = 160 items.
3. If 7 identical machines produce 70 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
140
The 7 machines produce 70 items per hour, so in 2 hours they produce 70 × 2 = 140 items.
4. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
630
The 6 machines produce 90 items per hour, so in 7 hours they produce 90 × 7 = 630 items.
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
192
The 4 machines produce 32 items per hour, so in 6 hours they produce 32 × 6 = 192 items.
6. If 3 identical machines produce 39 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
78
The 3 machines produce 39 items per hour, so in 2 hours they produce 39 × 2 = 78 items.
7. If 4 identical machines produce 36 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
216
The 4 machines produce 36 items per hour, so in 6 hours they produce 36 × 6 = 216 items.
8. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
60
The 2 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
9. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
48
The 2 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
10. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
196
The 2 machines produce 28 items per hour, so in 7 hours they produce 28 × 7 = 196 items.
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
168
The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
12. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?
64
The 2 machines produce 8 items per hour, so in 8 hours they produce 8 × 8 = 64 items.

12 questions · Seed 42 · 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 30 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
2. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
3. If 7 identical machines produce 70 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
4. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
6. If 3 identical machines produce 39 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
7. If 4 identical machines produce 36 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
8. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
9. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
10. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
12. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?

12 questions · Seed 42 · 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 30 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
90
The 2 machines produce 30 items per hour, so in 3 hours they produce 30 × 3 = 90 items.
2. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
160
The 4 machines produce 20 items per hour, so in 8 hours they produce 20 × 8 = 160 items.
3. If 7 identical machines produce 70 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
140
The 7 machines produce 70 items per hour, so in 2 hours they produce 70 × 2 = 140 items.
4. If 6 identical machines produce 90 items in 1 hour, how many items will 6 machines produce in 7 hours at the same rate?
630
The 6 machines produce 90 items per hour, so in 7 hours they produce 90 × 7 = 630 items.
5. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
192
The 4 machines produce 32 items per hour, so in 6 hours they produce 32 × 6 = 192 items.
6. If 3 identical machines produce 39 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
78
The 3 machines produce 39 items per hour, so in 2 hours they produce 39 × 2 = 78 items.
7. If 4 identical machines produce 36 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
216
The 4 machines produce 36 items per hour, so in 6 hours they produce 36 × 6 = 216 items.
8. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
60
The 2 machines produce 12 items per hour, so in 5 hours they produce 12 × 5 = 60 items.
9. If 2 identical machines produce 24 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
48
The 2 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
10. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 7 hours at the same rate?
196
The 2 machines produce 28 items per hour, so in 7 hours they produce 28 × 7 = 196 items.
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
168
The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
12. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 8 hours at the same rate?
64
The 2 machines produce 8 items per hour, so in 8 hours they produce 8 × 8 = 64 items.

12 questions · Seed 42 · Age guidance, not curriculum certification