# Related Rates Problem

• Nov 12th 2009, 02:54 PM
StarlitxSunshine
Related Rates Problem
A trough is 15ft long adn 4ft across the top. Its ends are isosceles trianngles with height 3ft. Water runs into the trough at the rate of 2.5 $\displaystyle ft^3$/min. How fast is the water level rising when it is 2 ft deep?

[The figure is an upside down triangular prism with the information above & water being "poured in" from a cup]

Okay...I tried to put down all the information I have:

the amount of water, lets say "l" -- > l=2ft
dl/dt is what we're looking for.
dV/dt = 2.5

Now I'm supposed to use an equation to figure this out. That's where I'm stuck.
• Nov 12th 2009, 03:18 PM
skeeter
Quote:

Originally Posted by StarlitxSunshine
A trough is 15ft long adn 4ft across the top. Its ends are isosceles trianngles with height 3ft. Water runs into the trough at the rate of 2.5 $\displaystyle ft^3$/min. How fast is the water level rising when it is 2 ft deep?

[The figure is an upside down triangular prism with the information above & water being "poured in" from a cup]

Okay...I tried to put down all the information I have:

the amount of water, lets say "l" -- > l=2ft
dl/dt is what we're looking for.
dV/dt = 2.5

Now I'm supposed to use an equation to figure this out. That's where I'm stuck.

volume of water in the tank is $\displaystyle V = \frac{1}{2} b h \cdot 15$

note also the similar triangles at the end of the trough ...

$\displaystyle \frac{b}{h} = \frac{4}{3}$

get the water volume in terms of $\displaystyle h$, and then take the derivative w/r to time.