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 14 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
2. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
3. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
4. If 4 identical machines produce 60 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
6. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
7. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
8. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
9. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
10. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
11. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
12. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?

12 questions · Seed 53 · 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 14 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
126
The 2 machines produce 14 items per hour, so in 9 hours they produce 14 × 9 = 126 items.
2. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
300
The 5 machines produce 75 items per hour, so in 4 hours they produce 75 × 4 = 300 items.
3. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
70
The 2 machines produce 14 items per hour, so in 5 hours they produce 14 × 5 = 70 items.
4. If 4 identical machines produce 60 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
540
The 4 machines produce 60 items per hour, so in 9 hours they produce 60 × 9 = 540 items.
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
405
The 3 machines produce 45 items per hour, so in 9 hours they produce 45 × 9 = 405 items.
6. 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.
7. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
168
The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
8. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
504
The 4 machines produce 56 items per hour, so in 9 hours they produce 56 × 9 = 504 items.
9. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
100
The 5 machines produce 50 items per hour, so in 2 hours they produce 50 × 2 = 100 items.
10. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
416
The 8 machines produce 104 items per hour, so in 4 hours they produce 104 × 4 = 416 items.
11. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
945
The 7 machines produce 105 items per hour, so in 9 hours they produce 105 × 9 = 945 items.
12. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
637
The 7 machines produce 91 items per hour, so in 7 hours they produce 91 × 7 = 637 items.

12 questions · Seed 53 · 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 14 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
2. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
3. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
4. If 4 identical machines produce 60 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
6. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
7. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
8. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
9. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
10. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
11. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
12. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?

12 questions · Seed 53 · 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 14 items in 1 hour, how many items will 2 machines produce in 9 hours at the same rate?
126
The 2 machines produce 14 items per hour, so in 9 hours they produce 14 × 9 = 126 items.
2. If 5 identical machines produce 75 items in 1 hour, how many items will 5 machines produce in 4 hours at the same rate?
300
The 5 machines produce 75 items per hour, so in 4 hours they produce 75 × 4 = 300 items.
3. If 2 identical machines produce 14 items in 1 hour, how many items will 2 machines produce in 5 hours at the same rate?
70
The 2 machines produce 14 items per hour, so in 5 hours they produce 14 × 5 = 70 items.
4. If 4 identical machines produce 60 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
540
The 4 machines produce 60 items per hour, so in 9 hours they produce 60 × 9 = 540 items.
5. If 3 identical machines produce 45 items in 1 hour, how many items will 3 machines produce in 9 hours at the same rate?
405
The 3 machines produce 45 items per hour, so in 9 hours they produce 45 × 9 = 405 items.
6. 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.
7. If 3 identical machines produce 42 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
168
The 3 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
8. If 4 identical machines produce 56 items in 1 hour, how many items will 4 machines produce in 9 hours at the same rate?
504
The 4 machines produce 56 items per hour, so in 9 hours they produce 56 × 9 = 504 items.
9. If 5 identical machines produce 50 items in 1 hour, how many items will 5 machines produce in 2 hours at the same rate?
100
The 5 machines produce 50 items per hour, so in 2 hours they produce 50 × 2 = 100 items.
10. If 8 identical machines produce 104 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
416
The 8 machines produce 104 items per hour, so in 4 hours they produce 104 × 4 = 416 items.
11. If 7 identical machines produce 105 items in 1 hour, how many items will 7 machines produce in 9 hours at the same rate?
945
The 7 machines produce 105 items per hour, so in 9 hours they produce 105 × 9 = 945 items.
12. If 7 identical machines produce 91 items in 1 hour, how many items will 7 machines produce in 7 hours at the same rate?
637
The 7 machines produce 91 items per hour, so in 7 hours they produce 91 × 7 = 637 items.

12 questions · Seed 53 · Age guidance, not curriculum certification