College Algebra, Chapter 1, 1.2, Section 1.2, Problem 54

Suppose that Jan and Levi can mow the lawn in $40$ min if they work together. If Levi works twice as fast as Jan, how long does it take Jan to mow the lawn alone?

If we let $x$ be the amount of time it takes Jan to do the job, the amount of time it takes Levi to the same job is $\displaystyle \frac{x}{2}$ so..


$
\begin{equation}
\begin{aligned}

\frac{1}{x} + \frac{1}{\displaystyle \frac{x}{2}} =& \frac{1}{40}
&& \text{Model}
\\
\\
\frac{1}{x} + \frac{2}{x} =& \frac{1}{40}
&& \text{Combine like terms}
\\
\\
\frac{1 + 2}{x} =& \frac{1}{40}
&& \text{Simplify by cross multiplication}
\\
\\
120 =& x
&&

\end{aligned}
\end{equation}
$


Thus, it takes $120$ min for Jan to mow the lawn alone.