$2.$ A tank initially holds $200$ gal of a brine solution containing $1$ lb of salt. At $\backslash (\backslash$mathrm$\{$t$\}=0\backslash )$ another brine solution containing $2$ lb of salt per gallon is poured into the tank at the rate of $\backslash (5\backslash$mathrm$\{$gal$\}/\backslash$mathrm$\{$min$\}\backslash ),$ while the well$-$stirred mixture leaves the tank at the same rate. Find $($a$)$ the amount of salt in the tank at any time $\backslash ($ t $\backslash )$ and $($b$)$ the time at which the mixture in the tank contains $4$ lb of salt.