# The cupcake machines: visual puzzle and solution | SwaVid

Five identical machines make five cupcakes in five minutes. Working at the same rate, how long will 100 machines take to make 100 cupcakes?

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# The cupcake machines

## The 100 machines take 5 minutes.

### Find the rate of one machine

### Scale machines and output together

### Keep the cycle time unchanged

SwaVid visual puzzle

Five identical machines make five cupcakes in five minutes. Working at the same rate, how long will 100 machines take to make 100 cupcakes?

Detailed solution

The machines work in parallel. Adding machines adds cupcake-making capacity at the same rate.

If five machines make five cupcakes in five minutes, each machine makes one cupcake during those five minutes.

One hundred machines can each make one cupcake at the same time. Together, they make 100 cupcakes in one five-minute production cycle.

The amount of work per machine has not changed, so the time per machine has not changed either.

Multiplying the five minutes by 20 assumes one set of five machines must do all the work. The extra machines are working simultaneously, not waiting in a queue.

- 1 Find the rate of one machine If five machines make five cupcakes in five minutes, each machine makes one cupcake during those five minutes. 5 cupcakes ÷ 5 machines = 1 cupcake per machine in 5 minutes
- 2 Scale machines and output together One hundred machines can each make one cupcake at the same time. Together, they make 100 cupcakes in one five-minute production cycle. 100 machines × 1 cupcake = 100 cupcakes
- 3 Keep the cycle time unchanged The amount of work per machine has not changed, so the time per machine has not changed either. 1 production cycle = 5 minutes

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