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Rate of change and integrating factor

  1. Sep 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Initially 5 grams of salt are dissolved in 20 liters of water. Brine with concentration of salt 2 grams of salt per lter is added at a rate of 3 liters per minute. The tank is mixed well and is drained at 3 liters a minute. How long does the process have to continue until there are 20 grams of salt in the tank?

    2. Relevant equations
    Rate in / Rate out

    Concentration = mass / Volume

    3. The attempt at a solution
    Rate in = 3L /min
    Concentration in =2 g/L

    rate out =3L /min
    Concentration out =x g/L

    I set change of concentration as x'
    x' = lim Δt→0 (3 L/ min * 2 g/L *Δt - 3 L/ min * x g/L *Δt) / V *Δt
    so x' = (3*2 - 3*x) / V where V =20 L (given)

    x' = 3/10 - 3x/20

    then use integrating factor, but I have different answer what am I doing wrong? thank
  2. jcsd
  3. Sep 20, 2016 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    What is your answer? Maybe it is not wrong at all, but we cannot tell without seeing it.
  4. Sep 20, 2016 #3
    I have x(t) = 2 - 7/4 EXP (-3/20 t)
    which then gives t = 3.73 min
    for 20 gram salt in the water (concentration 1 g/L)

    But the answer said to be 40/3 ln(4/3) which is 3.84 min
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