Answer
See explanations.
Work Step by Step
Step 1. Let $R(t)$ be the rate of increase in gal/min (it is a continuous function).
Step 2. In 24 hours ($\Delta t=1440min$), the volume increased by 1400 acre-ft, which is equivalent to $\Delta V=1400\times43560\times7.48=456,160,320~gal$
Thus the average rate of increase is $\bar R=\frac{\Delta V}{\Delta t}=316,778gal/min$
Step 3. The Mean Value Theorem implies that during $0\leq t\leq1440min$, there must be a time such that $R(t)=\bar R=316,778\gt 225,000gal/min$
