A particular bullet train accelerates and decelerates at the rate of $10$ ft$/$s$.$Its maximum cruising speed is $75$ mi$/$h $($Round your answers to three decimal places.$)$ What is the maxium distance in miles that the train can travel if it accelerated from rest until it reached its crusing speed and then runs at that speed for $20$ minutes?

Suppose that the train starts from rest and must come to a complete stop in $20$ minutes. What is the maximum distance in miles it can travel under these conditions?

Find the minimum time in minutes that the train takes to travel between two consecutivr stations that are $37\mathrm{.}5$ miles apart.

The trip from one station to the next takes at minimum $37\mathrm{.}5$ minutes. How far in miles apart are the stations?