A mixed flow reactor is filled with $10$ L of an aqueous solution in which A is dissolved. When the concentration of A in the reactor is $1$ mol$/$L$,$ the aqueous solution containing A in the concentration is supplied to the reactor at a rate of $0\mathrm{.}1$ mol$/$L at $2$ L$/$min and the aqueous solution is extracted from the reactor at the same rate of $2$ L$/$min$.$ In this case, calculate the time taken for the concentration of A in the reactor to decrease to $10\%$ of the initial concentration for each of the following. However, assume that there is no change in the density of the aqueous solution depending on the concentration.

$(1)$ If A does not react

$(2)$ A decreases to $-$r$\_$A$($mol$/$L $$ min$)=0\mathrm{.}2($min$-1)$ C$\_$A$($mol$/$L$)$