Question

Two people can paint a house in $14$ hours. Working individually, one of the people takes $2$ hours more than it takes the other person to paint the house. How long would it take each person working individually to paint the house? (approx)

• A. $29$ hrs
• B. $30$ hrs
• C. $28$ hrs
• D. None of these

Answer 1

The correct option is A $29$ hrs

Two people working together = 14 hours
Let the people can paint a house be x.
Working individually, one people takes 2 hours more than it takes the other person to paint = $\frac{1}{x}+\frac{1}{x+2}$
So, $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{14}$
$\frac{2x+2}{x^2+2x}=\frac{1}{14}$
$28x+28=x^2+2x$
$x^2-26x-28$
Using quadratic formula, $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find the roots of the quadratic equation
$\Rightarrow \frac{26\pm \sqrt{(-26{)}^2-4\times 1\times (-28)}}{2\times 1}$
$\Rightarrow \frac{26\pm \sqrt{788}}{2}$
$\Rightarrow \frac{26\pm 28.07}{2}$
$x=27.03$, $x=-1.03$
x cannot be negative.
Each person working individually to paint the house = 27 + 2 = 29 hours.