Answer
32 hours and 24 minutes
Work Step by Step
Let the amount of time it takes for Jim's hose to fill the pool be x. The amount of time it takes for Bob's hose to fill the pool is then $\frac{4x}{5}$. Therefore, in 1 hour, Jim fills $\frac{1}{x}$ of the pool, Bob fills$ \frac{5}{4x}$ of the pool, and they fill $\frac{1}{18}$ of the pool working together.
From here, we can set up an equation:
$\frac{1}{x} + \frac{5}{4x} = \frac{1}{18}$
$\frac{9}{4x} = \frac{1}{18}$
$3x = 162$
$x = 40.5$
Since x is 40.5, the amount of time it takes for Bob's hose to fill the pool is $\frac{4 \times 40.5}{5} = 32.4$, or 32 hours and 24 minutes.
