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 9 hours at the same rate?
2. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
3. If 3 identical machines produce 18 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
5. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
6. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
8. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
9. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
10. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
11. If 5 identical machines produce 15 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
12. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?

12 questions · Seed 104730 · 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 9 hours at the same rate?
270
The 2 machines produce 30 items per hour, so in 9 hours they produce 30 × 9 = 270 items.
2. 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.
3. If 3 identical machines produce 18 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
54
The 3 machines produce 18 items per hour, so in 3 hours they produce 18 × 3 = 54 items.
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
108
The 3 machines produce 36 items per hour, so in 3 hours they produce 36 × 3 = 108 items.
5. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
135
The 3 machines produce 27 items per hour, so in 5 hours they produce 27 × 5 = 135 items.
6. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
728
The 8 machines produce 104 items per hour, so in 7 hours they produce 104 × 7 = 728 items.
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
144
The 4 machines produce 24 items per hour, so in 6 hours they produce 24 × 6 = 144 items.
8. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
120
The 4 machines produce 20 items per hour, so in 6 hours they produce 20 × 6 = 120 items.
9. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
104
The 4 machines produce 52 items per hour, so in 2 hours they produce 52 × 2 = 104 items.
10. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
72
The 2 machines produce 12 items per hour, so in 6 hours they produce 12 × 6 = 72 items.
11. If 5 identical machines produce 15 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
30
The 5 machines produce 15 items per hour, so in 2 hours they produce 15 × 2 = 30 items.
12. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
66
The 2 machines produce 22 items per hour, so in 3 hours they produce 22 × 3 = 66 items.

12 questions · Seed 104730 · 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 9 hours at the same rate?
2. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
3. If 3 identical machines produce 18 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
5. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
6. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
8. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
9. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
10. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
11. If 5 identical machines produce 15 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
12. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?

12 questions · Seed 104730 · 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 9 hours at the same rate?
270
The 2 machines produce 30 items per hour, so in 9 hours they produce 30 × 9 = 270 items.
2. 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.
3. If 3 identical machines produce 18 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
54
The 3 machines produce 18 items per hour, so in 3 hours they produce 18 × 3 = 54 items.
4. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
108
The 3 machines produce 36 items per hour, so in 3 hours they produce 36 × 3 = 108 items.
5. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
135
The 3 machines produce 27 items per hour, so in 5 hours they produce 27 × 5 = 135 items.
6. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
728
The 8 machines produce 104 items per hour, so in 7 hours they produce 104 × 7 = 728 items.
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
144
The 4 machines produce 24 items per hour, so in 6 hours they produce 24 × 6 = 144 items.
8. If 4 identical machines produce 20 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
120
The 4 machines produce 20 items per hour, so in 6 hours they produce 20 × 6 = 120 items.
9. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
104
The 4 machines produce 52 items per hour, so in 2 hours they produce 52 × 2 = 104 items.
10. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
72
The 2 machines produce 12 items per hour, so in 6 hours they produce 12 × 6 = 72 items.
11. If 5 identical machines produce 15 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
30
The 5 machines produce 15 items per hour, so in 2 hours they produce 15 × 2 = 30 items.
12. If 2 identical machines produce 22 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
66
The 2 machines produce 22 items per hour, so in 3 hours they produce 22 × 3 = 66 items.

12 questions · Seed 104730 · Age guidance, not curriculum certification