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cpx
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[SOLVED] Classic watertank equation
I'm having trouble with a variant of the classic watertank equation. The data is as follows.
A tank contains 300 liters of saline water, containing a total of 1800 grams of salt. Through an inlet, saline water containing 5 grams/liter is pumped in at a speed of 2 liters/minute. The well-mixed solution is pumped out at a speed of 3 liters/minute. Compute the quantity of salt, in grams, after 100 minutes.
Here's my attempt at solving this:
[tex]
V(t)=300-t
[/tex]
[tex]
\frac{dS}{dt}=10t-3\frac{S}{V}
[/tex]
[tex]
S(0)=1800
[/tex]
Running it in the ODE Analyzer in MAPLE got me [tex]S(100)\approx33867[/tex], which isn't the solution. Can anyone spot what I've done wrong?
I'm having trouble with a variant of the classic watertank equation. The data is as follows.
A tank contains 300 liters of saline water, containing a total of 1800 grams of salt. Through an inlet, saline water containing 5 grams/liter is pumped in at a speed of 2 liters/minute. The well-mixed solution is pumped out at a speed of 3 liters/minute. Compute the quantity of salt, in grams, after 100 minutes.
Here's my attempt at solving this:
[tex]
V(t)=300-t
[/tex]
[tex]
\frac{dS}{dt}=10t-3\frac{S}{V}
[/tex]
[tex]
S(0)=1800
[/tex]
Running it in the ODE Analyzer in MAPLE got me [tex]S(100)\approx33867[/tex], which isn't the solution. Can anyone spot what I've done wrong?