Chapter 12.6, Problem 10P

To determine

To find:time taken by James to paint the house himself.

Answer to Problem 10P

Time took by James was $8h$ to paint the house himself where $h$ is an hour.

Explanation of Solution

Given information:

Colleen took $2h$ less than James on working alone and when working together they both took $10h$ to paint the house.

Formula:

The quadratic equation $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Calculation:

Consider that the time taken by James to paint the house was $xh$ where $h$ is an hour.

As mentioned above Colleen took $2h$ less than James on working alone.

Therefore Colleen took $\left(x-2\right)h$ where $h$ is anhour.

When they worked together they both took $10h$ to paint the house.

Therefore $x^2+{\left(x-2\right)}^2={10}^2$ .

Therefore

  $\begin{array}{l}{x}^2+{\left(x-2\right)}^2={10}^2\Rightarrow x^2+x^2+4-4x=100\Rightarrow x^2-2x-48=0\\ \Rightarrow x^2+6x-8x-48=0\Rightarrow x\left(x+6\right)-8\left(x+6\right)=0\Rightarrow \left(x-8\right)\left(x+6\right)=0\\ \Rightarrow x=8,-6.\end{array}$

Therefore the James took $8h$ to paint the house himself where $h$ is an hour.