(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Beer containing 6% alcohol per gallon is pumped into a vat that initially contains 350 gallons of beer at 3% alcohol. The rate at which the beer is pumped in is 3 gallons per minute, whereas the mixed liquid is pumped out at a rate of 4 gallons per minute. Find the number of gallons of alcohol A(t) in the tank at any time. What is the percentage of alcohol in the tank after 60 minutes?

2. Relevant equations

dA/dt = rate in - rate out

A is the number of gallons of alcohol in the tank

3. The attempt at a solution

dA/dt = rate in - rate out = 0.06r - (r*A)/(350-t)

I'm not sure about my setup because so far we've only worked with problems in which the volume doesn't constantly change, ie 250 gallons in the tank at all times with r(in) = r(out) = 3 gal/min rather than this problem where r(in) = 3 gal/min and r(out) = 4 gal/min and the volume of liquid in the tank decreases by 1 gal/min

I've worked the problem from the initial conditions:

A(0) = 10.5 gallons

to be:

A(t) = (21-t)*exp[-rln(350-t)] - 21*exp[-r-ln(350)] +10.5

but I'm seriously doubting what I've done so far because there's nowhere to check my answers, and my method seems to make this problem far more complicated then my professor ever makes his problems.

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# Differential equations problem, flow rates, constantly changing volume

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