Water flows into a tank at the variable rate $R_{\scriptsize{\text{in}}} = \frac{48}{1 + t}$ gal/min and out at the constant rate $R_{\scriptsize{\text{out}}} = 6$ gal/min. Let $V(t)$ be the volume of water in the tank at time $t$.

(a) Set up a differential equation for $V(t)$ and solve it with the initial condition $V(0) = 80$.
$V(t) =$

(b) Find the maximum value of $V$.
maximum value of $V =$ gal