A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour??
Give it a try guys!! lol
My two favorite things in life are Beer and differential equations!
You will have 4.9% alcohol after one hour.
And I would wait at least another hour before having a glass.
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Hey Wilberchie, You may want to rethink your answer. There is no way, if you are adding 6% alcohol, that you can end up with 7% or more. Think about it. Good luck. A Hypertopology Intended for Functional Differential Equations::
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Solve amount of alcohol in beer.
500 * .04 = 20 gal of alcohol in beer
Solve amount of alcohol entering
5 * 0.06 = 0.3 gal of alcohol entering
use the equation
dx/dt = k
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dx = change in alcohol content
dt = change in time
k = rate of alcohol entering
dx = kdt
∫ dx from 20 to x= 0.3∫ dt from 0 to 60
x - 20 = 0.3 (60 - 0)
x = 38
since we have constant volume in the vat,
we can compute the percentage of alcohol
38/500 *100 = 7.6% alcohol after 1 hr
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Separable Equations and Beer!?