A tank with a capacity of 900 gal originally contains 200 gal of water with 100

Question

A tank with a capacity of 900 gal originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/min. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. Find the concentration (in pounds per gallon) of salt in the tank when it is on the point of overflowing. Compare this concentration with the theoretical limiting concentration if the tank had infinite capacity.

Explanation / Answer

(a) y(t) = 3t - 2((100 + 3t)/(200 + 3t)) +100 (b) C(t) = (100 +3t)/(200 +3t) (c) concentration limit would be 1 lb per gallon although it will never reach that point it will be getting closer and closer to that point.

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