Question

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

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 $\frac{1}{15}$

The rate that Sammy and Nolan together paint the house is $\frac{1}{9}$

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

Thus, we have;

$Rate=\frac{1}{9}-\frac{1}{15}$

$Rate=\frac{5-3}{45}$

$Rate=\frac{2}{45}$

Thus, the rate that it would take Nolan to paint the house by himself is $\frac{2}{45}$

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

$Total \ houses=Rate \times Time$

Substituting the values, we have;

    $1=\frac{2}{45} \times t$

  $\frac{45}{2}=t$

$22.5=t$

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