
Related rates, again
I need help with this question on my assignment:
a water trough is $\displaystyle 10m$ long and a crosssection has the shape of an isosceles triangle that is $\displaystyle 1m$ across at the top and is $\displaystyle 50cm$ high. The trough is being filled with water at a rate of $\displaystyle 0.4m^3/min$. How fast will the water level rise when the water is $\displaystyle 40cm$ deep?
Please and thank you.

The volume of water in the tank at a water level $\displaystyle h$ is $\displaystyle V = \frac{1}{2}(10)bh$. Where $\displaystyle b = 2h$ is the width of the water at the surface.
So $\displaystyle \frac{dV}{dt} = \frac{d(10h^2)}{dt} = 20h\frac{dh}{dt} = .4$.
Therefore $\displaystyle \frac{dh}{dt} = \frac{.4}{20h}$ and at $\displaystyle h=.4$ this is exactly $\displaystyle \frac{dh}{dt}=\frac{1m}{20sec}$