91Ó°ÊÓ

(a)

Given Data:

The capacity of the swimming pool is \(V = 80000\;{\rm{L}}\)

The flow rate of water from garden hose is \(q = 60\;{\rm{L}}/\min \)

The flow rate of moderate size river is \(Q = 5000\;{{\rm{m}}^3}/{\rm{s}}\)

The flow rate of water is the volume of the water passing through the garden hose in per second.

The time to fill the swimming pool by garden hose is given as:

\(t = \frac{V}{q}\)

Here,\(t\)is the duration to fill swimming pool by garden hose

\(\begin{aligned}t &= \frac{{80000\;{\rm{L}}}}{{60\;{\rm{L}}/\min }}\\t &= 1333.33\;\min \end{aligned}\)

Therefore, the time to fill the swimming pool by garden hose is \(1333.33\;\min \).

(b)

The time to fill the swimming pool by moderate size river is given as:

\(T = \frac{V}{Q}\)

Here,\(t\)is the duration to fill the swimming pool by a garden hose

\(\begin{aligned}T &= \frac{{\left( {80000\;{\rm{L}}} \right)\left( {\frac{{1\;{{\rm{m}}^3}}}{{1000\;{\rm{L}}}}} \right)}}{{5000\;{{\rm{m}}^3}/{\rm{s}}}}\\T &= 1.6 \times {10^{ - 2}}\;{\rm{sec}}\end{aligned}\)

Therefore, the time to fill the swimming pool by moderate size river is \(1.6 \times {10^{ - 2}}\;{\rm{sec}}\).