Two 100 litre tanks are completely lled 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. Tank B 100 Litres Tank A 100 Litres Pure water The problem is to nd the amount of salt (in kilograms) in Tank A and Tank B at time t. (a) Let 3203) 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 (:1) =(-3s _3:3;)(:)- (b) Find explicit formulas for :r(t) and y(t) at time t given that (-33: is ) ( i) = _0.12( i) and (-as is )( a) = o.os(; ). ((3) Conrm that the concentration of salt in each tank approaches zero over a long period of time