Two tanks are connected as in Figure 1.6. Tank 1 initially

Chapter 1, Problem 1.47

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Two tanks are connected as in Figure 1.6. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into tank 2 at the rate of 5 gallons per minute, and tank 2 also has an output of 5 gallons per minute. Determine the amount of salt in each tank at any time. Also, determine when the concentration of salt in tank 2 is a minimum and how much salt is in the tank at that time. Hint: Solve for the amount of salt in tank 1 at time t and use this solution to help determine the amount in tank 2.