A $12\mathrm{.}5m^3$ tank is being filled with water at a rate of $0\mathrm{.}05\frac{m^3}{s}.$ At a moment

when the tank contains $1\mathrm{.}2m^3$ water, a bottom leak develops and gets

progressively worse with time. The rate of leakage can be approximated as

$0\mathrm{.}0025t(\frac{m^3}{s}),$ where $t(s)$ is the time from the moment leak begins.

a$.$ Find the expression for the volume of liquid water in terms of time using

Laplace transforms.

b$.$ how long will it take for the compute emptying of tank$?$