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 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
2. If 3 identical machines produce 24 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
3. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
4. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
5. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
6. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
7. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
9. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
10. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
11. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
12. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

12 questions · Seed 55 · 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 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.
2. If 3 identical machines produce 24 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
120
The 3 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
3. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
168
The 7 machines produce 21 items per hour, so in 8 hours they produce 21 × 8 = 168 items.
4. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
168
The 6 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
5. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
36
The 2 machines produce 12 items per hour, so in 3 hours they produce 12 × 3 = 36 items.
6. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
128
The 4 machines produce 16 items per hour, so in 8 hours they produce 16 × 8 = 128 items.
7. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
84
The 2 machines produce 28 items per hour, so in 3 hours they produce 28 × 3 = 84 items.
8. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
104
The 2 machines produce 26 items per hour, so in 4 hours they produce 26 × 4 = 104 items.
9. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
672
The 8 machines produce 112 items per hour, so in 6 hours they produce 112 × 6 = 672 items.
10. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
384
The 8 machines produce 48 items per hour, so in 8 hours they produce 48 × 8 = 384 items.
11. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
108
The 2 machines produce 18 items per hour, so in 6 hours they produce 18 × 6 = 108 items.
12. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
144
The 6 machines produce 36 items per hour, so in 4 hours they produce 36 × 4 = 144 items.

12 questions · Seed 55 · 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 45 items in 1 hour, how many items will 3 machines produce in 4 hours at the same rate?
2. If 3 identical machines produce 24 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
3. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
4. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
5. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
6. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
7. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
9. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
10. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
11. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
12. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?

12 questions · Seed 55 · 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 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.
2. If 3 identical machines produce 24 items in 1 hour, how many items will 3 machines produce in 5 hours at the same rate?
120
The 3 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
3. If 7 identical machines produce 21 items in 1 hour, how many items will 7 machines produce in 8 hours at the same rate?
168
The 7 machines produce 21 items per hour, so in 8 hours they produce 21 × 8 = 168 items.
4. If 6 identical machines produce 42 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
168
The 6 machines produce 42 items per hour, so in 4 hours they produce 42 × 4 = 168 items.
5. If 2 identical machines produce 12 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
36
The 2 machines produce 12 items per hour, so in 3 hours they produce 12 × 3 = 36 items.
6. If 4 identical machines produce 16 items in 1 hour, how many items will 4 machines produce in 8 hours at the same rate?
128
The 4 machines produce 16 items per hour, so in 8 hours they produce 16 × 8 = 128 items.
7. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
84
The 2 machines produce 28 items per hour, so in 3 hours they produce 28 × 3 = 84 items.
8. If 2 identical machines produce 26 items in 1 hour, how many items will 2 machines produce in 4 hours at the same rate?
104
The 2 machines produce 26 items per hour, so in 4 hours they produce 26 × 4 = 104 items.
9. If 8 identical machines produce 112 items in 1 hour, how many items will 8 machines produce in 6 hours at the same rate?
672
The 8 machines produce 112 items per hour, so in 6 hours they produce 112 × 6 = 672 items.
10. If 8 identical machines produce 48 items in 1 hour, how many items will 8 machines produce in 8 hours at the same rate?
384
The 8 machines produce 48 items per hour, so in 8 hours they produce 48 × 8 = 384 items.
11. If 2 identical machines produce 18 items in 1 hour, how many items will 2 machines produce in 6 hours at the same rate?
108
The 2 machines produce 18 items per hour, so in 6 hours they produce 18 × 6 = 108 items.
12. If 6 identical machines produce 36 items in 1 hour, how many items will 6 machines produce in 4 hours at the same rate?
144
The 6 machines produce 36 items per hour, so in 4 hours they produce 36 × 4 = 144 items.

12 questions · Seed 55 · Age guidance, not curriculum certification