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 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
3. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
4. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
5. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
6. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
8. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
9. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
10. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
11. 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. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

12 questions · Seed 104729 · 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 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
693
The 7 machines produce 77 items per hour, so in 9 hours they produce 77 × 9 = 693 items.
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
539
The 7 machines produce 77 items per hour, so in 7 hours they produce 77 × 7 = 539 items.
3. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
840
The 7 machines produce 105 items per hour, so in 8 hours they produce 105 × 8 = 840 items.
4. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
32
The 2 machines produce 8 items per hour, so in 4 hours they produce 8 × 4 = 32 items.
5. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
48
The 4 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
6. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
480
The 8 machines produce 80 items per hour, so in 6 hours they produce 80 × 6 = 480 items.
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
216
The 4 machines produce 24 items per hour, so in 9 hours they produce 24 × 9 = 216 items.
8. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
240
The 3 machines produce 30 items per hour, so in 8 hours they produce 30 × 8 = 240 items.
9. 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.
10. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
390
The 5 machines produce 65 items per hour, so in 6 hours they produce 65 × 6 = 390 items.
11. 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. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
192
The 8 machines produce 24 items per hour, so in 8 hours they produce 24 × 8 = 192 items.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
3. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
4. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
5. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
6. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
8. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
9. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
10. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
11. 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. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Combined work-rate puzzles

Answers and reasoning. Review before teaching.

1. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
693
The 7 machines produce 77 items per hour, so in 9 hours they produce 77 × 9 = 693 items.
2. If 7 identical machines produce 77 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
539
The 7 machines produce 77 items per hour, so in 7 hours they produce 77 × 7 = 539 items.
3. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
840
The 7 machines produce 105 items per hour, so in 8 hours they produce 105 × 8 = 840 items.
4. If 2 identical machines produce 8 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
32
The 2 machines produce 8 items per hour, so in 4 hours they produce 8 × 4 = 32 items.
5. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 2 hours at the same rate?
48
The 4 machines produce 24 items per hour, so in 2 hours they produce 24 × 2 = 48 items.
6. If 8 identical machines produce 80 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
480
The 8 machines produce 80 items per hour, so in 6 hours they produce 80 × 6 = 480 items.
7. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
216
The 4 machines produce 24 items per hour, so in 9 hours they produce 24 × 9 = 216 items.
8. If 3 identical machines produce 30 items in 1 hour, how many items will 3 machines produce in 8 hours at the same rate?
240
The 3 machines produce 30 items per hour, so in 8 hours they produce 30 × 8 = 240 items.
9. 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.
10. If 5 identical machines produce 65 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
390
The 5 machines produce 65 items per hour, so in 6 hours they produce 65 × 6 = 390 items.
11. 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. If 8 identical machines produce 24 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
192
The 8 machines produce 24 items per hour, so in 8 hours they produce 24 × 8 = 192 items.

12 questions · Seed 104729 · Age guidance, not curriculum certification