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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Combined work-rate puzzles

Take your time. Show your thinking.

1. If 2 identical machines produce 10 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
2. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
4. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
5. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
6. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
7. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
9. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
10. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
11. If 6 identical machines produce 30 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
12. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?

12 questions · Seed 46 · 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 10 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
30
The 2 machines produce 10 items per hour, so in 3 hours they produce 10 × 3 = 30 items.
2. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
36
The 3 machines produce 12 items per hour, so in 3 hours they produce 12 × 3 = 36 items.
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
56
The 2 machines produce 28 items per hour, so in 2 hours they produce 28 × 2 = 56 items.
4. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
120
The 4 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
5. 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.
6. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
120
The 6 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
7. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
48
The 2 machines produce 16 items per hour, so in 3 hours they produce 16 × 3 = 48 items.
8. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
54
The 3 machines produce 27 items per hour, so in 2 hours they produce 27 × 2 = 54 items.
9. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
288
The 8 machines produce 72 items per hour, so in 4 hours they produce 72 × 4 = 288 items.
10. 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.
11. If 6 identical machines produce 30 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
180
The 6 machines produce 30 items per hour, so in 6 hours they produce 30 × 6 = 180 items.
12. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
490
The 7 machines produce 98 items per hour, so in 5 hours they produce 98 × 5 = 490 items.

12 questions · Seed 46 · 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 10 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
2. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
4. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
5. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 6 hours at the same rate?
6. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
7. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
8. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
9. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
10. If 5 identical machines produce 25 items in 1 hour, how many items will 5 machines produce in 5 hours at the same rate?
11. If 6 identical machines produce 30 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
12. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?

12 questions · Seed 46 · 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 10 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
30
The 2 machines produce 10 items per hour, so in 3 hours they produce 10 × 3 = 30 items.
2. If 3 identical machines produce 12 items in 1 hour, how many items will 3 machines produce in 3 hours at the same rate?
36
The 3 machines produce 12 items per hour, so in 3 hours they produce 12 × 3 = 36 items.
3. If 2 identical machines produce 28 items in 1 hour, how many items will 2 machines produce in 2 hours at the same rate?
56
The 2 machines produce 28 items per hour, so in 2 hours they produce 28 × 2 = 56 items.
4. If 4 identical machines produce 24 items in 1 hour, how many items will 4 machines produce in 5 hours at the same rate?
120
The 4 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
5. 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.
6. If 6 identical machines produce 24 items in 1 hour, how many items will 6 machines produce in 5 hours at the same rate?
120
The 6 machines produce 24 items per hour, so in 5 hours they produce 24 × 5 = 120 items.
7. If 2 identical machines produce 16 items in 1 hour, how many items will 2 machines produce in 3 hours at the same rate?
48
The 2 machines produce 16 items per hour, so in 3 hours they produce 16 × 3 = 48 items.
8. If 3 identical machines produce 27 items in 1 hour, how many items will 3 machines produce in 2 hours at the same rate?
54
The 3 machines produce 27 items per hour, so in 2 hours they produce 27 × 2 = 54 items.
9. If 8 identical machines produce 72 items in 1 hour, how many items will 8 machines produce in 4 hours at the same rate?
288
The 8 machines produce 72 items per hour, so in 4 hours they produce 72 × 4 = 288 items.
10. 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.
11. If 6 identical machines produce 30 items in 1 hour, how many items will 6 machines produce in 6 hours at the same rate?
180
The 6 machines produce 30 items per hour, so in 6 hours they produce 30 × 6 = 180 items.
12. If 7 identical machines produce 98 items in 1 hour, how many items will 7 machines produce in 5 hours at the same rate?
490
The 7 machines produce 98 items per hour, so in 5 hours they produce 98 × 5 = 490 items.

12 questions · Seed 46 · Age guidance, not curriculum certification