Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of 5 L/min. The brine solution is pumped from tank 1 into tank 2 at a rate of 15 L/min, and from tank 2 into tank 1 at a rate of 10 L/min. A brine solution flows out the bottom of tank 2 at a rate of 5 L/min. Suppose there are 80 Lof brine in tank 1 and 180 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes, and y the amount of salt, in kilograms, in tank 2 after t minutes. Assume that each tank is mixed perfectly. If x(0)=5 kg and y(0)=4 kg, how much is salt in each tank after t minutes? As t→∞, how much salt is in tank 1? How much salt is in tank 2?
Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of 5 L/min. The brine solution is pumped from tank 1 into tank 2 at a rate of 15 L/min, and from tank 2 into tank 1 at a rate of 10 L/min. A brine solution flows out the bottom of tank 2 at a rate of 5 L/min. Suppose there are 80 Lof brine in tank 1 and 180 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes, and y the amount of salt, in kilograms, in tank 2 after t minutes. Assume that each tank is mixed perfectly.
If x(0)=5 kg and y(0)=4 kg, how much is salt in each tank after t minutes? As t→∞, how much salt is in tank 1? How much salt is in tank 2?
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