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Homework Help: Find the quantity Q(t) of salt in the tank?

  1. Jan 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A tank initially contains 40 gallons of pure water. A solution with 1 gram of salt per gallon of water is added to the tank at 3 gal/min, and the resulting solution dranes out at the same rate. Find the quantity Q(t) of salt in the tank at time t>0.

    2. Relevant equations

    3. The attempt at a solution
    I don't know how to set up the differential equation for this problem.
  2. jcsd
  3. Jan 13, 2015 #2
    Let V be the volume of liquid in the tank in gal, q be the rate at which liquid is entering (and leaving) the tank in gal/min, and C(t) be the concentration of salt within the tank in gm/gal at time t. Based on this, at time t, how much salt is in the tank? If the tank is well mixed, what is the rate that salt is leaving the tank? What is the rate that salt is entering the tank? Write a balance of input - output = rate of accumulation.

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