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 9 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
5. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
6. If 2 identical machines produce 30 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
7. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
8. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?
9. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
10. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
12. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?

12 questions · Seed 104732 · 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 9 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
63
The 3 machines produce 9 items per hour, so in 7 hours they produce 9 × 7 = 63 items.
2. 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.
3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
234
The 2 machines produce 26 items per hour, so in 9 hours they produce 26 × 9 = 234 items.
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
540
The 5 machines produce 60 items per hour, so in 9 hours they produce 60 × 9 = 540 items.
5. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
96
The 6 machines produce 24 items per hour, so in 4 hours they produce 24 × 4 = 96 items.
6. If 2 identical machines produce 30 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
150
The 2 machines produce 30 items per hour, so in 5 hours they produce 30 × 5 = 150 items.
7. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
125
The 5 machines produce 25 items per hour, so in 5 hours they produce 25 × 5 = 125 items.
8. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?
144
The 6 machines produce 72 items per hour, so in 2 hours they produce 72 × 2 = 144 items.
9. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
112
The 4 machines produce 16 items per hour, so in 7 hours they produce 16 × 7 = 112 items.
10. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
288
The 3 machines produce 36 items per hour, so in 8 hours they produce 36 × 8 = 288 items.
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
294
The 3 machines produce 42 items per hour, so in 7 hours they produce 42 × 7 = 294 items.
12. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
150
The 5 machines produce 25 items per hour, so in 6 hours they produce 25 × 6 = 150 items.

12 questions · Seed 104732 · 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 9 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
2. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
5. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
6. If 2 identical machines produce 30 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
7. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
8. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?
9. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
10. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
12. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?

12 questions · Seed 104732 · 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 9 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
63
The 3 machines produce 9 items per hour, so in 7 hours they produce 9 × 7 = 63 items.
2. 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.
3. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
234
The 2 machines produce 26 items per hour, so in 9 hours they produce 26 × 9 = 234 items.
4. If 5 identical machines produce 60 items in 1 hour, how many items will 5 machines produce in 9 hours at the same rate?
540
The 5 machines produce 60 items per hour, so in 9 hours they produce 60 × 9 = 540 items.
5. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
96
The 6 machines produce 24 items per hour, so in 4 hours they produce 24 × 4 = 96 items.
6. If 2 identical machines produce 30 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
150
The 2 machines produce 30 items per hour, so in 5 hours they produce 30 × 5 = 150 items.
7. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
125
The 5 machines produce 25 items per hour, so in 5 hours they produce 25 × 5 = 125 items.
8. If 6 identical machines produce 72 items in 1 hour, how many items will 6 machines produce in 2 hours at the same rate?
144
The 6 machines produce 72 items per hour, so in 2 hours they produce 72 × 2 = 144 items.
9. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 7 hours at the same rate?
112
The 4 machines produce 16 items per hour, so in 7 hours they produce 16 × 7 = 112 items.
10. If 3 identical machines produce 36 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
288
The 3 machines produce 36 items per hour, so in 8 hours they produce 36 × 8 = 288 items.
11. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 7 hours at the same rate?
294
The 3 machines produce 42 items per hour, so in 7 hours they produce 42 × 7 = 294 items.
12. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
150
The 5 machines produce 25 items per hour, so in 6 hours they produce 25 × 6 = 150 items.

12 questions · Seed 104732 · Age guidance, not curriculum certification