The Great Lakes: Assume that Lake Erie has a volume of 480 km^3, and that that t

Question

The Great Lakes: Assume that Lake Erie has a volume of 480 km^3, and that that the rate of inflow (into Lake Erie) from Lake Huron and outflow into Lake Ontario (from Lake Erie) are both 350 km^3 per year, and also that the outflow and inflow are perfectly mixed. At one time the pollutant concentration of Lake Erie was five times that of Lake Huron. The industries causing the pollution of Lake Erie at that time were ordered to cease. How long did it take to reduce the pollution concentration in Lake Erie to twice that of Lake Huron?

Explanation / Answer

concentration of pollution in lake Huron=p/km3

initial concentration of pollutants in lake errie=5p/km3

final concentration of pollutants in lake errie=2p/km3

rate of inflow of pollutants into lake errie=350 km3/year *(p/km3)

net pollutants after addition=5p*480 +p*350 =(2750 p)

concentration of pollutants after inflow=(2750 p) /(480+350)=(2750 p) /830=3.3 p/km3

net outflow of pollutants=350 km3*(3.3 p)/km3=(1159.6 p)

the pollutants that remain in lake errie( each year)=2750p-1159.6p=1590.4 p

So concentration of pollutants after outflow=1590.4 p/480 km3=3.3 p

Reduction of pollutant concentration per year=5p-3.3p=1.7p

So ,time for reduction of concentration to 2p =2/1.7=1.2 yr=1.2 yr*12months/yr=14 months

Answer=14 months or 1.2 years

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