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A 200 liter tank initially contains 100 liters of water with a salt concentration of 0.1 grams per liter.

Water with a salt concentration of 0.5 grams per liter flows into the tank at a rate of 20 liters per

minute. Assume that the fluid is mixed instantaneously and that this well-mixed fluid is pumped out

at a rate of 10 liters per minute. Let c (t) and

v(t), be the concentration of salt and the volume of

water in the tank at time t (in minutes), respectively. Then,

v`(t)=10

v(t) c`(t) +20c(t)=10

a) Solve these differential equations to find the particular solutions for v(t) and c(t).

b) What is the concentration of salt in the tank when the tank first overflows?

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