# Math Help - Related rates, again

1. ## Related rates, again

I need help with this question on my assignment:

a water trough is $10m$ long and a cross-section has the shape of an isosceles triangle that is $1m$ across at the top and is $50cm$ high. The trough is being filled with water at a rate of $0.4m^3/min$. How fast will the water level rise when the water is $40cm$ deep?

Please and thank you.

2. The volume of water in the tank at a water level $h$ is $V = \frac{1}{2}(10)bh$. Where $b = 2h$ is the width of the water at the surface.

So $\frac{dV}{dt} = \frac{d(10h^2)}{dt} = 20h\frac{dh}{dt} = .4$.

Therefore $\frac{dh}{dt} = \frac{.4}{20h}$ and at $h=.4$ this is exactly $\frac{dh}{dt}=\frac{1m}{20sec}$