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## Homework Statement

## The Attempt at a Solution

I think that problems such as this one tend to take on the rough form of [itex]\frac{dQ}{dt} = rate in - rate out[/itex]. I suppose I should treat each lake such that is has it's own equation regarding concentration. I reasoned that, in the case of the first lake, the rate of change in quantity as time changes, call it [itex]\frac{dQ}{dt}[/itex] has no real rate in. In this case, it was more like there was an immediate "lump sum" of toxins released into the lake with no further toxins after that point. Then is the equation for the first lake not given by [itex]\frac{dQ}{dt} = \frac{-Q}{100,000 + 500t}(500)[/itex]? I write the +500t because the toxin is becoming more and more diluted as time progresses (because of clean water inflow).

With regard to the second lake's concentration, call it [itex]\frac{dY}{dt}[/itex], it's inflow should be the same as the 1st lake's outflow, no? Thus, write that [itex]\frac{dY}{dt} = \frac{Q}{100,000 + 500t}(500) - \frac{Y}{200,000 + 500t}[/itex].

Now, this is just the way that I tried to reason out how to write the differential equations. Since the rest of the problem relies on these, I think I should get my answers checked before I push onward.