Example $3$: A tank is initially filled with $(100$ gal $)$ of salt solution containing $(1l\frac{b}{g}al).$ Fresh brine water containing $(2l\frac{b}{g}al)$ run into the tank at a rate of $(5ga\frac{l}{m}in),$ and the mixture is assumed to be uniform then it runs out at the same rate. Find the amount of salt in the tank at any time, then determine how long will it take for the amount of salt to be $(150$ lb $).$