Rate of change of a triangular prisim

[Megrs]

Homework Statement

A trough is 15ft long and 4ft wide. Its ends are isosceles triangles with a height of 3ft. Water runs into the trough at the rate of 2.5ft^3/min. How fast is the water level rising when it is 2ft deep?

Homework Equations

V= .5lwh

The Attempt at a Solution

since l would be constant would dV/dt= (15/2)w(dh/dt) + (15/2)h (dw/dt) ? but then 2.5=(15/2)(8/3)(dh/dt) + (15/2)(2)(dw/dt) how do i find dh/dt without dw/dt?

 

[Mark44]

Draw a picture of the end of the trough, if you haven't already done so.

At some time t, the water will be at a level of h feet. Use similar triangles to get an equation for the width w of the water across the end of the trough in terms of h.

 

[Megrs]

Draw a picture of the end of the trough, if you haven't already done so.

At some time t, the water will be at a level of h feet. Use similar triangles to get an equation for the width w of the water across the end of the trough in terms of h.

Thank you!