#### 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.