(Solved): 4. Two 100 litre tanks are completely filled with a mixture of salt and water with each tank contai ...

4. Two 100 litre tanks are completely filled with a mixture of salt and water with each tank containing a different concentration of salt. Fresh water is pumped into Tank A at a rate of 8 litres per minute. The water mixes in the two tanks as described by the diagram below, with water being pumped out of Tank B at a rate of 8 litres per minute. Initially Tank A contains no salt and Tank B contains 6kg of salt. 8L/min 9 L/min Tank B Pure water Tank A 100 Litres 100 Litres 1 L/min 8L/min The problem is to find the amount of salt (in kilograms) in Tank A and Tank B at time t. (a) Let z(t) be the amount of salt in Tank A at time t and let y(t) be the amount of salt (in kilograms) in Tank B at time t minutes. Explain why ()=( -0.09 0.01 0.09 -0.09 (*). (b) Find explicit formulas for r(t) and y(t) at time t given that -0.09 0.01 -0.09 0.01 ) (-3) = -0.12(3) and (- (?) = -0.06(³). 0.09 -0.09 0.09 -0.09 (c) Confirm that the concentration of salt in each tank approaches zero over a long period of time.