Answer
It would take 6.8 minutes to fill the pool.
Work Step by Step
We can find the volume flow rate of the water in the hose. The volume flow rate is the water speed times the cross-sectional area of the hose as:
$flow~rate = v~A$
$flow~rate = v~\pi~r^2$
$flow~rate = (3.0~m/s)(\pi)(0.0125~m)^2$
$flow~rate = 1.47\times 10^{-3}~m^3/s$
We can convert the volume flow rate to units of liters as:
$flow~rate = (1.47\times 10^{-3}~m^3/s)(\frac{1000~L}{1~m^3})$
$flow~rate = 1.47~L/s$
We can find the time it takes to fill the pool as:
$t = \frac{volume}{flow~rate}$
$t = \frac{600~L}{1.47~L/s}$
$t = 408~s = 6.8~min$
It would take 6.8 minutes to fill the pool.
