Question

Sammy can paint the house by himself in 15 hours. With Nolan's help, it only takes 9 hours.

How long would it take for Nolan to paint the house by himself?​

Answer 1

Given:

Sammy can paint the house by himself in 15 hours. With Nolan's help, it only takes 9 hours.

We need to determine the time it would take for Nolan to paint the house by himself.

Time taken by Nolan:

Let the rate that Sammy can paint the house by himself is
`(1)/(15)`

The rate that Sammy and Nolan together paint the house is
`(1)/(9)`

To determine the rate that it takes for Nolan to paint the house by himself is to subtract the rates.

Thus, we have;

`Rate=(1)/(9)-(1)/(15)`

`Rate=(5-3)/(45)`

`Rate=(2)/(45)`

Thus, the rate that it would take Nolan to paint the house by himself is
`(2)/(45)`

The time that it takes for Nolan to paint the house by himself can be determined using the formula,

`Total \ houses=Rate * Time`

Substituting the values, we have;

`1=(2)/(45) * t`

`(45)/(2)=t`

`22.5=t`

Thus, Nolan takes 22.5 hours to paint the house by himself.