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Math Help - easy tank mixing problem

  1. #1
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    easy tank mixing problem

    A five gallon tank is full of water. We open a spigot so 1 gal. leaves the tank and
    introduce a mixture of 1/2 lb. per gal at 1 gal per minute. Assuming the mixture is
    well mixed, what’s the concentration at time t?


    i did these a while ago but cant seem to remember how to finish them... based on my notes, i know to do something like
    dA/dt= concentration in- concentration out

    so, dA/dt= 1/2 - A/5, where A is gallons of water in the tank at time t. also, the initial condition is A(0)=5

    I could guess where to go from here, but I'd rather have someone help me with the rest of it before i learn it the wrong way myself.


    EDIT: just took a stab at it and got A=5/2 + 5/2 e^-1/5t
    i still cant remember how i used to do these, so im not sure if thats right..
    Last edited by twostep08; May 1st 2011 at 08:35 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by twostep08 View Post
    A five gallon tank is full of water. We open a spigot so 1 gal. leaves the tank and
    introduce a mixture of 1/2 lb. per gal at 1 gal per minute. Assuming the mixture is
    well mixed, what’s the concentration at time t?


    i did these a while ago but cant seem to remember how to finish them... based on my notes, i know to do something like
    dA/dt= concentration in- concentration out

    so, dA/dt= 1/2 - A/5, where A is gallons of water in the tank at time t. also, the initial condition is A(0)=5

    I could guess where to go from here, but I'd rather have someone help me with the rest of it before i learn it the wrong way myself.


    EDIT: just took a stab at it and got A=5/2 + 5/2 e^-1/5t
    i still cant remember how i used to do these, so im not sure if thats right..
    Try working with the mass of the solute (or whatever it is) rather than the concentration, then at any time the concentration is mass/5 lb/gal.

    CB
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