Find the time(s) if any when the tanks have the same amount of salt to within 0.

Question

Find the time(s) if any when the tanks have the same amount of salt to within 0.01 pounds. Give the time(s) and the amount. Explain your procedure. Find the limit of x and y as t approaches infinity. Explain your answer in terms of the physical model. Initially Tank A contains initially 50 gallons of water and 5 pounds of dissolved salt. Tank B contains initially 40 gallons of water and 1 pound of dissolved salt. Pure water is flowing into tank A at a rate of 2 gal / min and the solution in tank B is flowing into a third #tank at a rate of 2 gal / min. There is a flow of 3 gal / min from tank A to tank B and a flow of 1 gal / min from tank B to tank A. Both tanks are kept well-stirred. Let x be the amount of salt in tank A and y be the amount of salt in tank B. Make a diagram showing the two tanks and flows, with the flow rates and initial conditions labeled.

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