Answer
See below
Work Step by Step
From part a, we found: $V(x)=15.7x^2$
Since the pool is already half full, only $\frac{4}{5}-\frac{1}{2}=\frac{3}{10}$ of the pool needs to be filled.
Substitute: $V(x)=\frac{3}{10}\times15.7\times x^2=\frac{3}{10}\times15.7\times 11.98^2\approx675.981$
The time it takes to dispense 675.84 cubic feet of water is:
$(104+128.8)t=675.981\\
\rightarrow 232.8t=675.981\\
\rightarrow t\approx 2.9$
Hence, the total time it takes to fill $\frac{4}{5}$ of the pool is $2.9+8.8=11.7$ hours.
