A 1000 L holding tank that catches runoff from some chemical process initially has 200 L of water with 4 g of pollution dissolved in it. Polluted water flows into the tank at a rate of 4 L/hr and contains 4 g/L of pollution in it. A well-mixed solution leaves the tank at 2 L/hr. a. At what time is the tank going to overflow? b. Build a differential equation showing the connection of rate of change of amount of pollution in the tank and the time. c. Solve the differential equation to find the amount of pollution S in terms of t and use it to find the amount of pollution in the tank when it is filled with half of its full capacity.
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We need to find the time when the tank overflows. The tank has an initial volume of 200 L and a capacity of 1000 L. The net rate of water flowing into the tank is 4 L/hr (inflow) - 2 L/hr (outflow) = 2 L/hr. Show more…
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