Water is added to a $300$ liter tank at varying flow rates. When the drain valve is opened

The flow rate of water from here is directly proportional to the height in the tank $($or the volume in the tank$).$ to the tank

The flow rate is gradually increased until it reaches the tank mouth when it is stable at $60$ liters$/$min$.$

It fills up$,$ but there is no overflow. Then the feed is suddenly reduced to $20$ litres$/$min$.$

a$)$ Write the equation that determines the relationship between the discharge rate q and the water volume V in the tank, and

Using this equation, calculate the volume at steady state when the inlet flow is $20$ liters $/$ min.

b$)$ The differential balance required for water, from the moment the flow is reduced, until the volume becomes stable.

For the elapsed time, write $($the equation should be dV$/$dt $=)$

c$)$ Find the required expression for V $($t$)$ by integrating the expression in b$.$