# Differential Equations Compartmental Analysis Word Problem

1. Jul 17, 2012

### pwood

Hello, I am trying to tackle a word problem in differential equations, but the setup has flummoxed me. Thank you in advance to any advice/help given.

1. The problem statement, all variables and given/known data

Beginning at time t  0, fresh water is pumped at
the rate of 3 gal/min into a 60-gal tank initially filled
with brine. The resulting less-and-less salty mixture
overflows at the same rate into a second 60-gal tank
that initially contained only pure water, and from
there it eventually spills onto the ground. Assuming
perfect mixing in both tanks, when will the water in
the second tank taste saltiest? And exactly how salty
will it then be, compared with the original brine?

2. Relevant equations
ds/dt = input - output

du/dt = previous output - output

3. The attempt at a solution
I have included a picture of a scratch piece of paper I am working on to demonstrate my work.

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2. Jul 17, 2012

### pwood

I should have mentioned that the stated answer is 20 minutes, for part one, and 1/e for part 2.