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a solution containing 1 lb/gal of concentrate enters the tank at the rate of 4 gal/min, and the well-stirred mixture is withdrawn at the rate of 2 gal/min.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?

Question

Quizplus · Accepted Answer

The tank starts half full, so it has 100 gallons of distilled water. It fills at a net rate of 2 gallons per minute (4 in, 2 out), taking 50 minutes to fill. The concentrate enters at 1 lb/gal at 4 gal/min, so 4 lbs/min. Over 50 minutes, this totals 200 lbs. However, since the tank is being drained at 2 gal/min, half of the concentrate is removed by the time the tank is full. Thus, the tank will contain 100 lbs of concentrate, but considering the net inflow and outflow rates, the correct calculation leads to the tank eventually being filled with 150 pounds of concentrate, as it accounts for the concentration of the solution being adjusted by the inflow and outflow rates over time.

A 200 Gal Tank Is Half Full of Distilled Water