Answer
$78\ gal$
Work Step by Step
Step 1. Based on the given conditions, we have $W(t)=kt$, where $k$ is a constant.
Step 2. At $t=5\ min$, we have $W(5)=30\ gal$. Thus $30=5k$ and $k=6\ gal/min$
Step 3. At $t=13\ min$, we have $W(13)=6(13)=78\ gal$
