Question

500-gallon tank initially contains 200 gallons of brine containing 100 pounds of dissolved salt. Brine containing 2 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon per minute. Set up a differential equation for the amount of salt A(t) in the tank at time t. How much salt is in the tank when it is full? (Round your answer to the 2 decimal places

Answer 1

We have

dA/dt = 2*4 - 1/(200+3t)
A(0) = 100

and we want to find A(100)

So, just solve the differential equation, and then plug in t=100, since at a net gain of 3 gal/min, the tank will be full at t=100.