Question

"joins" "together" Brad paints a house in 5 days. When his brother Nick joins him, they can paint a house in 3 days. How long does it take Nick to paint the house alone

Answer 1

7.5 days.

Explanation:

Let t represent time taken by Nick in days to paint the house alone.

Part of house painted by Nick in 1 day would be
`(1)/(t)`.

We have been given that Brad paints a house in 5 days, so part of house painted by Brad in 1 day would be
`(1)/(5)`.

We are also told that when Brad's brother Nick joins him, they can paint a house in 3 days. So part of house painted by both Brad and Nick together in 1 day would be
`(1)/(3)`.

Now, we will equate sum of work done by both brothers with
`(1)/(3)` to solve for t as:

`(1)/(t)+(1)/(5)=(1)/(3)`

`(1)/(t)* 15t+(1)/(5)* 15t=(1)/(3)* 15t`

`15+3t=5t`

`15+3t-3t=5t-3t`

`15=2t`

`2t=15`

`(2t)/(2)=(15)/(2)`

`t=7.5`

Therefore, it will take 7.5 days for the Nick to paint the house alone.