# 100 machines, 100 items: visual puzzle and solution | SwaVid

5 machines make 5 items in 5 minutes. How long do 100 machines take to make 100 items? See the complete step-by-step solution.

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# 100 machines, 100 items

## 5 minutes.

### Find one machine's rate

### Scale machines and items together

### Keep the time

SwaVid visual puzzle

5 machines make 5 items in 5 minutes. How long do 100 machines take to make 100 items?

Detailed solution

The machines work at the same time, not one after another.

Five machines make five items in five minutes, so each machine makes one item in five minutes.

100 machines each make one item in the same five minutes.

Each machine's workload is unchanged, so the time is unchanged.

Scaling 5 minutes up to 100 minutes treats the extra machines as if they were queued instead of running in parallel.

- 1 Find one machine's rate Five machines make five items in five minutes, so each machine makes one item in five minutes. 5 items ÷ 5 machines = 1 item each
- 2 Scale machines and items together 100 machines each make one item in the same five minutes. 100 × 1 item = 100 items
- 3 Keep the time Each machine's workload is unchanged, so the time is unchanged. Time = 5 minutes

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