There is a trough that is 10 meters long, 6 meters wide, and is in the shape of an equalateral triangle. The volume is changing at a rate of 0.2 m/s a second. The goal is to find the rate at which the height is changing at 2m.(adsbygoogle = window.adsbygoogle || []).push({});

So I initially set the problem up as V=0.5bhl (where b=width, h=height, and l=length).

Then I took the derivative of both sides & found

dv/dt=0.5bl(dh/dt)

From here I plugged in the numbers 0.2=0.5(10)(6)(dh/dt)

& found dh/dt=1/150.

However, I don't have a place to plug height in for 2m. So would it be correct to reason dh/dt is independent from the height? Or do I have something incorrect in my setup?

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# Homework Help: Related Rates Problem

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