# Question #f5a07

Jan 5, 2017

First, we must find out how much of the job remains and then how long the two will need.

#### Explanation:

The first sec. worked for 2 hours and so completed a fraction $\frac{2}{8} = \frac{1}{4}$ of the job, leaving $\frac{3}{4}$ of the job to do.
If they now both work for $x$ hours, the first will complete $\frac{x}{8}$ of the job and the second $\frac{x}{10}$.
So we need to solve $\frac{3}{4} = \frac{x}{8} + \frac{x}{10}$.

Multiplying both sides by 40 gives $30 = 5 x + 4 x = 9 x$.
And so $x = \frac{10}{3}$ hours or 3 hours and 20 minutes.