Answer to Question #244047 in Civil and Environmental Engineering for Fernando Matienzo

Question #244047
Situation 2
A tank initially contains 100 gal of brine where there is dissolved 20lb of salt. Starting at time t = 0, a
brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of 6gal/min is kept uniform
by stirring and the well-stirred mixture simultaneously flows out of the tank at a slower rate of 3gal/min.
1. How much salt is present at the end of 15 min?
2. How much salt is present after a long time?
Expert's answer

Let Q be the amount of sait in the tank and "dt\/dQ"

​ be the rate of change of amount in the tank

We get the equation as 

"\\space dt\/\ndQ\n\u200b\t\n + \n1\/20\n\n\u200b\t\n Q=0"

It is linear equation and the solution of it is "Q=Ce ^{-\\frac{t}{20}\nt}\n\u200b"

At t=0 , the value of Q is 20 


Therefore the equation is"\\space Q=Ce ^{-\\frac{t}{20}\nt}"

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