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 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
2. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
4. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
5. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
6. If 7 identical machines produce 56 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
7. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
8. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
9. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
10. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
11. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
12. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?

12 questions · Seed 43 · 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 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
132
The 3 machines produce 33 items per hour, so in 4 hours they produce 33 × 4 = 132 items.
2. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
80
The 4 machines produce 16 items per hour, so in 5 hours they produce 16 × 5 = 80 items.
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
210
The 6 machines produce 42 items per hour, so in 5 hours they produce 42 × 5 = 210 items.
4. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
54
The 2 machines produce 18 items per hour, so in 3 hours they produce 18 × 3 = 54 items.
5. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
784
The 8 machines produce 112 items per hour, so in 7 hours they produce 112 × 7 = 784 items.
6. If 7 identical machines produce 56 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
448
The 7 machines produce 56 items per hour, so in 8 hours they produce 56 × 8 = 448 items.
7. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
180
The 3 machines produce 45 items per hour, so in 4 hours they produce 45 × 4 = 180 items.
8. 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.
9. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
210
The 7 machines produce 105 items per hour, so in 2 hours they produce 105 × 2 = 210 items.
10. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
224
The 4 machines produce 32 items per hour, so in 7 hours they produce 32 × 7 = 224 items.
11. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
525
The 5 machines produce 75 items per hour, so in 7 hours they produce 75 × 7 = 525 items.
12. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
297
The 3 machines produce 33 items per hour, so in 9 hours they produce 33 × 9 = 297 items.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
2. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
4. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
5. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
6. If 7 identical machines produce 56 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
7. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
8. If 4 identical machines produce 52 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
9. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
10. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
11. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
12. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
132
The 3 machines produce 33 items per hour, so in 4 hours they produce 33 × 4 = 132 items.
2. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
80
The 4 machines produce 16 items per hour, so in 5 hours they produce 16 × 5 = 80 items.
3. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
210
The 6 machines produce 42 items per hour, so in 5 hours they produce 42 × 5 = 210 items.
4. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
54
The 2 machines produce 18 items per hour, so in 3 hours they produce 18 × 3 = 54 items.
5. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 7 hours at the same rate?
784
The 8 machines produce 112 items per hour, so in 7 hours they produce 112 × 7 = 784 items.
6. If 7 identical machines produce 56 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
448
The 7 machines produce 56 items per hour, so in 8 hours they produce 56 × 8 = 448 items.
7. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
180
The 3 machines produce 45 items per hour, so in 4 hours they produce 45 × 4 = 180 items.
8. 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.
9. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 2 hours at the same rate?
210
The 7 machines produce 105 items per hour, so in 2 hours they produce 105 × 2 = 210 items.
10. If 4 identical machines produce 32 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
224
The 4 machines produce 32 items per hour, so in 7 hours they produce 32 × 7 = 224 items.
11. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 7 hours at the same rate?
525
The 5 machines produce 75 items per hour, so in 7 hours they produce 75 × 7 = 525 items.
12. If 3 identical machines produce 33 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
297
The 3 machines produce 33 items per hour, so in 9 hours they produce 33 × 9 = 297 items.

12 questions · Seed 43 · Age guidance, not curriculum certification