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Suppose there are two lakes located on a stream. Clean water flows into the first lake, then...

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Advance Math

Suppose there are two lakes located on a stream. Clean waterflows into the first
lake, then the water from the first lake flows into the secondlake, and then water from the second
lake flows further downstream. The in and out flow from each lakeis 500 liters per hour. The first
lake contains 100 thousand liters of water and the second lakecontains 200 thousand liters of water.
A truck with 500 kg of toxic substance crashes into the first lake.Assume that the water is being
continually mixed perfectly by the stream.

a) Find the concentration of toxic substance as a function oftime in both lakes.
b) When will the concentration in the first lake be below 0.001 kgper liter?
c) When will the concentration in the second lake be maximal?

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