This problem has been perplexing me all week, it doesn't look hard but somehow I can't get the right answer. The question is -(adsbygoogle = window.adsbygoogle || []).push({});

A salt tank of capacity 500 gallons contains 200 gallons of water and 100 gallons of salt. Water is pumped into the tank at 3 gallon/min with salt of 1 lb/gallon. This is uniformly mixed, on the other end end water leaves the tank at 2 gallon/min. Setup a equation that predicts the amount of salt in the tank at any time up to the point when the tank overflows.

What I wrote was dy/dx = rate in - rate out

dy/dx = 3*1 - 2*Q(t)/(200+t)

Where Q(t) is the amount of salt in the tank. And 200+t represents the increasing volume of water in the tank. This equation doesn't give the correct answer, I have tried tacking 100 lbs of salt so that it becomes dy/dx = 3*1 - 2*(Q(t)+100)/(200+t)

but nothing seems to work. Can someone help me setup the correct equation?

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# Homework Help: Salt Tank - Differential Equation

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