The distance between two train stops is $1\mathrm{.}0$ miles. The average acceleration rate is $3\mathrm{.}0mp\frac{h}{second}$ and deceleration rate is $2\mathrm{.}0mp\frac{h}{second}.$ The top speed of the train is $45$ mph $.$ What is the shortest travel time $($in seconds$)$ between these two stops?

A$.97\mathrm{.}6$

B$.98\mathrm{.}6$

C$.99\mathrm{.}6$

D$.95\mathrm{.}6$