Problem 18E

18. If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume $V$ of water remaining in the tank after $t$ minutes as

$$ V=5000\left(1-\frac{1}{40} t\right)^{2} \quad 0 \in t \in 40 $$

Find the rate at which water is draining from the tank after

(a) $5 \mathrm{~min}$, (b) $10 \mathrm{~min}$, (c) $20 \mathrm{~min}$, and

(d) 40 min. At what time is the water flowing out the fastest? The slowest? Summarize your findings.

 

Step-by-Step Solution