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Math Help - Concentration Problem Revise Please

  1. #1
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    Concentration Problem Revise Please

    Question:

    A tank initally contains 60 gal of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h.

    a) Find the amount of salt in the tank after t mins.
    b) What is the maximum amount of salt ever in the tank?

    My solution to a) is attached, but how do I find b)? I took the derivative and set it equal to zero but find no real solutions...
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Question:

    A tank initally contains 60 gal of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h.

    a) Find the amount of salt in the tank after t mins.
    b) What is the maximum amount of salt ever in the tank?

    My solution to a) is attached, but how do I find b)? I took the derivative and set it equal to zero but find no real solutions...
    Sketch a graph of the solution (ha ha) over the domain 0 \leq t \leq 60 and look for the global maximum.

    By the way, the DE should be \frac{dx}{dt} = 2 - \left( \frac{3}{60 - t} \right) x.
    Last edited by mr fantastic; July 11th 2009 at 05:46 PM.
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