Question

Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?

Answer 1

18 Minutes

Explanation:

I did the test

Answer 2

18 Minutes

Explanation:

Simon and sophie each do a fraction of the job per minute like this:

-Simon does
`(1)/(30)` per minute (if we multiply this by 30 we have the completed job)

-Sophie does
`(1)/(45)` of the job per minute (again if we multiply this by 45 we have the completed job)

We will add this two to know how much of the job they do together in a minute:

`(1)/(30)+(1)/(45)=(1)/(18)`

They will do
`(1)/(18)` of the job per minute.

So the total time will be when they do
`(18)/(18)=1`, we can put this in one equation like this:

`(1)/(18)x=1`

where x is the total times we need to do
`(1)/(18)` of the job to complete it. We solve for x:

`x=18minutes`