2015 SRJC BT2 P1 Q10

Five hundred litres of salt solution is kept in a huge tank.

A man turns on a tap to allow salt solution containing \(250\) g of salt per litre of water to be poured into this tank at a rate of \(4\) litres/min. At the same time, the well-stirred solution is withdrawn from the tank at a rate of \(4\) litres/min.

It is known that there is \(50\)kg of salt dissolved in the salt solution before the tap is turned on.

Let \(y\) kg be the amount of salt in the tank at time \(t\) minutes after the tap is turned on.

1. Show that \(y\) satisfies the following differential equation
   \(\frac{\mathrm{d}y}{\mathrm{d}t}=1-\frac{y}{125}\)[3]
2. Find \(y\) in terms of \(t\).[4]
3. Find the amount of salt in the tank when \(t=20\).[1]
4. State what happens to \(y\) for large values of \(t\).[1]