Two tanks, each holding 10(a+) L of liquid, are interconnected by pipes, with the liquid flowing...

 

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Two tanks, each holding 10(a+ß) L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 4 L/min and from B into A at the same rate of 4 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.1 kg/L of salt flows into tank A at a rate of 6 L/min and a brine solution with a concentration of 0.2 kg/L of salt flows into tank B at a rate of 2 L/min. The (diluted) solution flows out of the system from tank A at 6 L/min and from tank B at 2 L/min. Assuming that, initially, tank A contains y kg of salt and tank B contains pure water, find the mass of salt in each tank at time t > 0. Two tanks, each holding 10(a+ß) L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 4 L/min and from B into A at the same rate of 4 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.1 kg/L of salt flows into tank A at a rate of 6 L/min and a brine solution with a concentration of 0.2 kg/L of salt flows into tank B at a rate of 2 L/min. The (diluted) solution flows out of the system from tank A at 6 L/min and from tank B at 2 L/min. Assuming that, initially, tank A contains y kg of salt and tank B contains pure water, find the mass of salt in each tank at time t > 0.

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Lets first write down the differential equations for the salt concentration in each tank using the l... View the full answer