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Question

A large tank contains 5 gallons of water with 6.25 pounds of salt dissolved in it. At the beginning of an experiment, a solution containing 1 pounds of salt per gallon of water is poured into the tank at the rate of 2 gallons per minute.

Find a formula for C(t), the concentration of salt (in pounds per gallon) in the solution in the tank t minutes after the beginning of the experiment.

C(t)=    

When does the concentration of salt in the tank reach 1.1 pounds per gallon?

t =    minutes.

Answer 1

Concentration = salt/gallons

Salt is added at the rate of 1 LBS/gallon * 2 gallons / minute = 2 LB/minute, which is 2t lbs in t minutes.

Water is added at the rate of 2 gallons / minute, which is 2t gallons in t minutes.

C(t) = (6.25 + 2t)/(5 + 2t)

C(t) = 1.1 = (6.25 + 2t)/(5 + 2t)

1.1(5+2t) = 6.25 + 2t

5.5 + 2.2t = 6.25 + 2t

.2t = .75

t = .75/.2 = 3.75 minutes.

Check it.

In 3.75 minutes the salt added is 2 * 3.75 = 7.5 lbs of salt.

The water added is 2 * 3.75 = 7.5 gallons of salt.

Salt / water = (6.25 + 7.5)/(5 + 7.5) = 13.75/12.5 = 1.1 lbs salt / gallon