A two-position mode controller is used to control the water level in a tank by opening or closing a valve which in the open position allows water at the rate of 0.4 m m 3 /  ys to enter the tank. The...

A two-position mode controller is used to control the water level in a tank by opening or closing a valve which in the open position allows water at the rate of 0.4 m m³/  ys to enter the tank. The tank has a cross-sectional area of 12 m²
and water leaves it at the constant rate of 0.2 m³/ ys. The valve opens when the water level reaches 4.0 m and closes at 4.4 m. What will be the times taken for (a) the valve opening to closing, (b) the valve closing to opening?