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Math Help - Mixed Concentration Problem, please revise.

  1. #1
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    Mixed Concentration Problem, please revise.

    I was tutoring and I wrote the solution to this mixed problem, but I do not have the same as the back of the text, please check and tell me what I do wrong.

    Question:

    A 400-gal tank initially contains 100 gal of brine containing 50 lbs of salt. Brine containing 1 lb of salt per gallon enters the tank at the rate of 5 gal/s, and the well-mixed brine in the tank flows out at the rate of 3 gal/s. How much salt will the tank contain when it is full of brine?

    Attached is the solution that I wrote.

    Thank you!!!
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  2. #2
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    \int\frac{3}{100+2t}dt=\frac{3}{2}ln(t+50)

    e^{\frac{3}{2}ln(t+50)}=(t+50)^{\frac{3}{2}}

    A(0)=50. Using the initial condition gives C=-12500\sqrt{2}

    I get A=2(t+50)-12500\sqrt{2}(t+50)^{\frac{-3}{2}}

    The tank initially has 100 gallons in it. It is flowing it at 5 gal/sec and out at 3 gal/sec

    That means it is gaining at 2 gal/sec and has 300 gallon to go.

    That will take 150 seconds.

    Plugging in t=150, gives 393.75

    Is that the book answer or did I make a mistake as well?. Easy to do.
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