MA$345$ Test la

$6)(10$ pts $)$ Mixture Problem. A brine solution of salt flows at a constant rate of $\backslash (5\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$min$\}\backslash )$ into a large tank that initially held $500$ L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at the same rate of $\backslash (5\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$min$\}\backslash ).$ If the concentration of salt in the brine entering the tank is $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$L$\}\backslash ),$ find the concentration equation $[$in kg$/$L$]$ for the mass of salt in the tank as a function of time $"$ t $"$ minutes. You may use the diagram to help collect your thoughts.

Things to consider: flow rate in$,$ flow rate out, initial condition, what variable letters you want to use, the concentration equation format, and solving method.