College Algebra, Chapter 1, 1.2, Section 1.2, Problem 56

Suppose that Jan and Levi use hoses from both houses to fill Jan's swimming pool. They know that it takes $18 h$ using both hoses. They also know that Jan's hose, when used alone, takes $20 \%$ less time than Levi' hose alone. Determine how much time is required to fill the pool by each hose alone?

If we let $x$ be the amount of time it takes Jan's hose to fill the pool alone, the amount of time it takes Levi's hose to fill the pool is $\displaystyle \frac{x}{0.80}$, so..


$
\begin{equation}
\begin{aligned}

\frac{1}{x} + \frac{1}{\displaystyle \frac{x }{0.80}} =& \frac{1}{18}
&& \text{Model}
\\
\\
\frac{1}{x} + \frac{0.80}{x} =& \frac{1}{18}
&& \text{Combine like terms}
\\
\\
\frac{1.80}{x} =& \frac{1}{18}
&& \text{Solve for } x
\\
\\
x =& 32.4 \text{ hours}
&&

\end{aligned}
\end{equation}
$


Thus, it takes $32.4$ hours for Jan's hose to fill the pool alone while it takes $\displaystyle \frac{32.4}{0.80} = 40.5$ for Levi's hose to fill the pool alone.