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 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
2. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
3. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
5. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
7. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
9. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
10. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
11. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

12 questions · Seed 50 · 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 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
162
The 3 machines produce 27 items per hour, so in 6 hours they produce 27 × 6 = 162 items.
2. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
648
The 8 machines produce 72 items per hour, so in 9 hours they produce 72 × 9 = 648 items.
3. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
336
The 4 machines produce 56 items per hour, so in 6 hours they produce 56 × 6 = 336 items.
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
180
The 5 machines produce 60 items per hour, so in 3 hours they produce 60 × 3 = 180 items.
5. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
96
The 8 machines produce 24 items per hour, so in 4 hours they produce 24 × 4 = 96 items.
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
72
The 4 machines produce 24 items per hour, so in 3 hours they produce 24 × 3 = 72 items.
7. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
120
The 4 machines produce 40 items per hour, so in 3 hours they produce 40 × 3 = 120 items.
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
576
The 8 machines produce 64 items per hour, so in 9 hours they produce 64 × 9 = 576 items.
9. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
120
The 2 machines produce 20 items per hour, so in 6 hours they produce 20 × 6 = 120 items.
10. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
182
The 7 machines produce 91 items per hour, so in 2 hours they produce 91 × 2 = 182 items.
11. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
220
The 5 machines produce 55 items per hour, so in 4 hours they produce 55 × 4 = 220 items.
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
640
The 8 machines produce 80 items per hour, so in 8 hours they produce 80 × 8 = 640 items.

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
2. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
3. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
5. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
7. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
9. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
10. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
11. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 6 hours at the same rate?
162
The 3 machines produce 27 items per hour, so in 6 hours they produce 27 × 6 = 162 items.
2. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
648
The 8 machines produce 72 items per hour, so in 9 hours they produce 72 × 9 = 648 items.
3. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 6 hours at the same rate?
336
The 4 machines produce 56 items per hour, so in 6 hours they produce 56 × 6 = 336 items.
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 3 hours at the same rate?
180
The 5 machines produce 60 items per hour, so in 3 hours they produce 60 × 3 = 180 items.
5. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
96
The 8 machines produce 24 items per hour, so in 4 hours they produce 24 × 4 = 96 items.
6. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
72
The 4 machines produce 24 items per hour, so in 3 hours they produce 24 × 3 = 72 items.
7. If 4 identical machines produce 40 items in 1 hour, how many items will 4 machines produce in 3 hours at the same rate?
120
The 4 machines produce 40 items per hour, so in 3 hours they produce 40 × 3 = 120 items.
8. If 8 identical machines produce 64 items in 1 hour, how many items will 8 machines produce in 9 hours at the same rate?
576
The 8 machines produce 64 items per hour, so in 9 hours they produce 64 × 9 = 576 items.
9. If 2 identical machines produce 20 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
120
The 2 machines produce 20 items per hour, so in 6 hours they produce 20 × 6 = 120 items.
10. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
182
The 7 machines produce 91 items per hour, so in 2 hours they produce 91 × 2 = 182 items.
11. If 5 identical machines produce 55 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
220
The 5 machines produce 55 items per hour, so in 4 hours they produce 55 × 4 = 220 items.
12. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
640
The 8 machines produce 80 items per hour, so in 8 hours they produce 80 × 8 = 640 items.

12 questions · Seed 50 · Age guidance, not curriculum certification