Respuesta :
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 [tex]\frac{1}{15}[/tex]
The rate that Sammy and Nolan together paint the house is [tex]\frac{1}{9}[/tex]
To determine the rate that it takes for Nolan to paint the house by himself is to subtract the rates.
Thus, we have;
[tex]Rate=\frac{1}{9}-\frac{1}{15}[/tex]
[tex]Rate=\frac{5-3}{45}[/tex]
[tex]Rate=\frac{2}{45}[/tex]
Thus, the rate that it would take Nolan to paint the house by himself is [tex]\frac{2}{45}[/tex]
The time that it takes for Nolan to paint the house by himself can be determined using the formula,
[tex]Total \ houses=Rate \times Time[/tex]
Substituting the values, we have;
[tex]1=\frac{2}{45} \times t[/tex]
[tex]\frac{45}{2}=t[/tex]
[tex]22.5=t[/tex]
Thus, Nolan takes 22.5 hours to paint the house by himself.
