Question

A 500-gallon tank initially contains 200 gallons of brine containing 85 pounds of dissolved salt. Brine containing 1 pounds of salt per gallon flows into the tank at the rate of 44 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

dx/dt=ri*ci-ro*co where x is amount of salt in tank.

but volume=200+(ri-ro)t=200+(44-1)t
= 200-43t
so dx/dt=44*1 -x/(200-43t) check that.
see http://math2.uncc.edu/~sjbirdso/diffyQ/handouts/mixture%20solution.pdf for the rest