Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure 5.2). The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 6 L/min. The (diluted) solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If, initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at a time $t ⩾ 0$ .

Question

Accepted Answer

The mass of salt in each tank at the time $t ⩾ 0$ is;

$x (t) = - (10 - \frac{20}{\sqrt{7}}) e^{(\frac{- 5 + \sqrt{7}}{100}) t} - (10 + \frac{20}{\sqrt{7}}) e^{(\frac{- 5 - \sqrt{7}}{100}) t} + 20$

and $y (t) = - \frac{30}{\sqrt{7}} e^{(\frac{- 5 + \sqrt{7}}{100}) t} + \frac{30}{\sqrt{7}} e^{(\frac{- 5 - \sqrt{7}}{100}) t} + 20$

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Short Answer