Suppose that a tank contains 1000 gallons of a water and sewage mixture. Initial

Question

Suppose that a tank contains 1000 gallons of a water and sewage mixture. Initially the concentration of the sewage is 0.1 pounds of sewage per gallon. Then valves are opened allowing sewage and water to flow in at a rate of 40 gallons per minute with 0.8 pounds of sewage per gallon. The tank is mixed and the mixture is allowed to flow out at a slower rate of 36 gallons per minute. Set up, do not solve, the differential equation for the amount of sewage, x, in the tank at time t. Also include the initial condition.

Explanation / Answer

initially amount of solids= 0.1*1000= 100 pounds

(1000+40t-36t)d(A(t))/dt = 40*0.8 - 36* A(t)

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