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## Homework Statement

A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/4 pound of salt per gallon is added to the tank at 4 gal/min, and the resulting mixture is drained out at 2 gal/min. Find the quantity of salt in the tank as it's about to overflow.

## Homework Equations

None.

## The Attempt at a Solution

(1/4)lbs/gal*(4)gal/min=1lbs/min

(Q)lbs/100 gal*(2)gal/min=Qlbs/50 min

dQ/dt=1-Q/50=(50-Q)/50

50/(50-Q)dQ=dt

-50ln abs(50-Q)=t+C

ln abs(50-Q)= -t/50+C

50-Q=Ce^(-t/50)

Q=50-Ce^(-t/50)

Q(0)=0

C=50

Q(t)=50(1-e^(-t/50))

Q(50)=31.606

But the answer is Q(50)=47.5

Where did I make a mistake?