Problems 33 through 37 illustrate the application of linear first-order differential equations to mixture problems.

Rework Example 4 for the case of Lake Ontario, which empties into the St. Lawrence River and receives inflow from Lake Erie (via the Niagara River). The only differences are that this lake has a volume of 1640 km³ and an inflow-outflow rate of 410 km³/year.

Example 4

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Example 4 Mixture problem Assume that Lake Erie has a volume of 480 km³ and that its rate of inflow (from Lake Huron) and outflow (to Lake Ontario) are both 350 km³ per year. Suppose that at the time t = 0 (years), the pollutant concentration of Lake Erie-caused by past industrial pollution that has now been ordered to cease-is five times that of Lake Huron. If the outflow henceforth is perfectly mixed lake water, how long will it take to reduce the pollution concentration in Lake Erie to twice that of Lake Huron?