A large tank is used to remove a small amount of precipitated solid particles $($impurities$)$ from a saline solution in a steady$-$state process. Normally a saline solution $(20\%$ by mass of salt$)$ is pumped by a single inlet stream into a tank at the rate of $10$ kg$/$min and a single outlet stream is established by pumping from the tank at the same flow rate. The normal operation of the process maintains the constant level, with a total mass in the tank of $1,000$ kg$,$ well below its maximum capacity. At a certain moment $($t $=0)$ an operator accidentally opens a valve, which supplies pure water that constantly flows into the tank at the speed of $10$ kg$/$min$,$ together with the saline solution feeding, so the tank level begins to rise. Determine the amount of water, mass and salt in the tank as a function of time during the first hour after opening the pure water valve. Assume that the flow rate out of the tank does not vary and that its contents are always well mixed