MORE related rates of EVIL!!!!

[BobbyJoeCool]

Extra Credit on the test (already taken)...

 

Here's the question:

 

You have a 5 meter long trough. A cross section of the trough is an isololes trapazoid with upper base 3 meters, lower base 2 meters and an altitude of 2 meters. You are pouring water into the trough at a rate of 1 cubic meter per second. What is the rate of change of the height of the water at a height of .5 meters...

 

here is what I got out for givens and the variable I need to solve for...

 

V'=1

l=5

b1=2

h=.5

h'=?

 

[math]V=\tfrac{b_{1}+b_{2}}{2} \cdot h \cdot l[/math]

 

b1 is 2, l=5, but I can't figure out b2! Then it's a simple matter of related rates, and diferentiate with respect to t...

 

[math]V'=\tfrac{2+b_{2}}{2}\cdot 5 \cdot h'[/math]

 

[math]1=\tfrac{2+b_{2}}{2}\cdot 5 \cdot h'[/math]

 

[math]h'=\frac{1}{\tfrac{2+b_{2}}{2}\cdot 5}[/math]

 

[math]h'=\frac{2}{5(2+b_{2})}[/math]

 

SO I'm this close, but can't figure out this b2 (which is probably something simple... and I just can't think... It's been too long since Geometry)

 

Can someone help me out (like pointing me in the right direction)?