Any help would be appreciated! A one cubic meter per second constant flow of water enters the rigid rectangular duct shown below

$($uniform cross sectional area from entry to exit$).$ Two of the surfaces of the duct are porous. Water is

constantly added through the upper surface of the duct at a rate shown by the parabolic curve $($the inflow

distribution per unit length varies parabolically from zero to a maximum value at the exit$),$ while water

constantly leaves through the front face $($coming out of the page towards you$)$ at a rate that decreases

linearly with distance $($the outflow distribution per unit length varies linearly from a maximum value at the

beginning to a value of zero at the exit$)$ from the entrance as shown. The maximum values of both flow

rates, shown in the sketch, are given in cubic meters per second per unit length along the duct. What is the

average velocity of water leaving through the exit of the duct if it is $1\mathrm{.}0$ m long and has a uniform

rectangular cross section of $0\mathrm{.}1m^2?$

Hint:

If the duct length is in the $x-$dimension:

Assume the expression for inflow through the porous top surface is given by: $Q_{\text{t}\text{o}\text{p}}={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}0\mathrm{.}3x^{2}dx$

Assume the expression for outflow through the porous front face is given by: $Q_{\text{f}\text{r}\text{o}\text{n}\text{t}}={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}0\mathrm{.}5(1-x)dx$