Solve the problem.
-A 200 gal tank is half full of distilled water. At time = 0, a solution containing 1 lb/gal of concentrate enters the tank at the rate of 4 gal/min, and the well-stirred mixture is withdrawn at the rate of 2 gal/min. When the tank
Is full, how many pounds of concentrate will it contain?
A) 100 pounds
B) 200 pounds
C) 120 pounds
D) 150 pounds

Question

Quizplus · Accepted Answer

The tank initially contains 100 gallons of water. Since the inflow rate is 4 gal/min and the outflow rate is 2 gal/min, the net inflow rate is 2 gal/min. It will take 50 minutes to fill the remaining 100 gallons. During this time, 4 gal/min of solution containing 1 lb/gal enters the tank, adding 4 lbs of concentrate per minute. Over 50 minutes, this results in 200 lbs of concentrate entering the tank. However, since the tank is being filled at a net rate of 2 gal/min, the concentration of the solution in the tank will be diluted. The final amount of concentrate in the tank when it is full is 150 pounds.

Solve the Problem. -A 200 Gal Tank Is Half Full of Distilled Water