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Math Help - when is the tank empty?

  1. #1
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    when is the tank empty?

    a large tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well mixed solution is pumped out at 10 gal/min. find the number A(t) of pounds of salt in the tank at time t.

    ok so I know dA/dt = rate in - rate out.

    so dA/dt = (2 lbs/gal)(5 gal/min) - ()???

    ok im stuck with how to figure out the rate out?

    my book is saying the rate out = 2A/(100-t)??? i dont see how the book came up with that answer...any thoughts?

    thanks in advance....
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  2. #2
    A Plied Mathematician
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    Rate out = (A/(total amount of liquid in gallons present at time t)) * (10 gal/min). The total amount of liquid is changing by a net amount of 5 gallons per minute, since the rate out is greater than the rate in. So you have (A/(500-5t))(10)=2A/(100-t). Voila.
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  3. #3
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    yea i think i need to practice more of these problems...thanks again.
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  4. #4
    A Plied Mathematician
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    You're welcome, as always.
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