Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg per litre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B at a rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are kept well stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1 in tank B. (a) Write down equations showing, respectively, the concentrations C1 and C2 in the tanks after t minutes. (b) Write down two differential equations to show how A1 and B1 vary with time. (c) What is the relation between A1 and B1? (d) Eliminate B1 between the two equations in (b) and solve the resulting equation for A1. (e) What is the concentration in tank A after 10 minutes?
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg per
litre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B at
a rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are kept
well stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1
in tank B.
(a) Write down equations showing, respectively, the concentrations C1 and C2 in
the tanks after t minutes.
(b) Write down two differential equations to show how A1 and B1 vary with time.
(c) What is the relation between A1 and B1?
(d) Eliminate B1 between the two equations in (b) and solve the resulting equation
for A1.
(e) What is the concentration in tank A after 10 minutes?
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