2. (35 Pts) An empty bathtub has its drain closed and is being filled with water from the faucet at a rate of 10 kg/min. After 10 minutes of filling the tub at this constant rate, the drain is opened and 4 kg/min flows out. At the same time, as the drain is opened, the inlet flow is reduced to 2kg/min. Make a plot of the mass of the water in the bathtub as a function of time.

Determine the time from the very beginning when the tub will be completely empty.