A body of water is polluted with mercury. The lake has a volume of 200 million c

Question

A body of water is polluted with mercury. The lake has a volume of 200 million cubic meters and mercury is present in a concentration of 5 grams per million cubic meters. Health officials state that any level above 1 g per million cubic meters is considered unsafe. If water unpolluted by mercury flows into the lake at a rate of 0.5 million cubic meters per day, and uniformly mixed lake water flows out of the lake at the same rate, how long will it take for the lake to reach a mercury concentration that is considered safe?

Explanation / Answer

Lake has volume = 200 million cubic meters

Mercury present = 5 grams per million cubic meters

Added unpolluted water in lake per day = 0.5 million cubic meters

Now let x days it will take to reach a mercury concentration that is considered safe case.

Firstly, total weight of mercury in lake water = 200×5 = 1000gm

Now after added unpolluted water for x days, added volume of unpolluted water = x(0.5) million cubic meters

Now concentration of mercury = 1000/(200+0.5x)

And it should be equal to 1g per million cubic meters for safe.

1000/(200+0.5x) = 1

1000 = 200+0.5x

0.5x = 800

x = 1600 days

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