Answer
It would take 140 hours to fill the pool up to a height of 1.4 meters.
Work Step by Step
We can convert the diameter of the hose to units of centimeters as:
$d = (\frac{5}{8}~in)(\frac{2.54~cm}{1~in}) = 1.6~cm$
We then find the volume flow rate in the hose, which is the flow speed times the cross-sectional area of the hose as:
$flow~rate = v~A$
$flow~rate = v~\pi~r^2$
$flow~rate = (0.40~m/s)(\pi)(0.80\times 10^{-2}~m)^2$
$flow~rate = 8.0\times 10^{-5}~m^3/s$
We then find the volume of the pool;
$V = \pi~R^2~h$
$V = (\pi)(3.05~m)^2(1.4~m)$
$V = 40.9~m^3$
We then find the time to fill the pool to a height of 1.4 meters:
$time = \frac{V}{flow~rate}$
$time = \frac{40.9~m^3}{8.0\times 10^{-5}~m^3/s}$
$time = 5.1\times 10^5~s$
Next, we convert the time to units of hours;
$time = (5.1\times 10^5~s)(\frac{1~hr}{3600~s})$
$time = 140~hours$
It would take 140 hours to fill the pool up to a height of 1.4 meters.
