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## Homework Statement

A trough is 9 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 8 inches deep?

Variables:

b=5 ft

h=1 ft

l=9 ft

## Homework Equations

v=(1/2)bhl

dv/dt=14

dh/dt=?

when h=2/3 ft

## The Attempt at a Solution

I tried doing it the straightforward way:

v=(1/2)bhl

dv/dt=(1/2)(5)(2/3)(dh/dt)(9)

14=(1/2)(5)(2/3)(dh/dt)(9)

dh/dt=14/15

This is wrong. Then I tried using similar triangles to get the new base to go along with the height of 8 in. For that I got 10/3 ft. So,

v=(1/2)bhl

dv/dt=(1/2)(10/3)(2/3)(dh/dt)(9)

14=(1/2)(10/3)(2/3)(dh/dt)(9)

dh/dt= 7/5

This is also incorrect. I really don't know why. Any help would be greatly appreciated!