Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt. Tank B contains 200 gallons of solution in which is dissolved 40 lbs of salt. Pure water flows into tank A at a rate of 5 gal/s. There is a drain at the bottom of tank A. The solution leaves tank A via this drain at a rate of 5 gal/s and flows immediately into tank B at the same rate. A drain at the bottom of tank B allows the solution to leave tank B at a rate of 2.5 gal/s. What is the salt content in tank B at the precise moment that tank B contains 250 gal of solution?
I do not know how to calculate the integrating factor because I'm getting an equation which has both a dx/dt - dy/dt. The solution to the whole problem would be helpful.
The solution is comprised of detailed explanations on how to set up the first order differential equation when there are two tanks connected together and solutions are filled in and flows out both tanks. It also shows how to solve the differential equations.