Problem $1(25$ Points$)$

You are a traffic analyst working at a motorsport event where four race cars are participating in a time trial on a $2\mathrm{.}5-$mile trioval track. Your job is to record and analyze the speed of each car as they pass a speed trap at a specific point on the track. The four race cars are traveling at constant speeds of $195m\frac{i}{h}r,190m\frac{i}{h}r,185m\frac{i}{h}r,$ and $180m\frac{i}{h}r,$ respectively.

You've been assigned to monitor the speed trap for $30$ minutes and are required to calculate two key metrics:

Time$-$mean speed: This reflects the average speed of the vehicles over the time they pass the speed trap.

Space$-$mean speed: This is the harmonic mean of the speeds, which gives insight into the average speed across a fixed section of the track.

Using the speed data collected from the cars passing the speed trap, calculate the time$-$mean speed and space$-$mean speed for the four vehicles during the $30-$minute period. In your analysis, explain the practical implications of these metrics in terms of traffic flow and race strategy.

$($Note: Pay attention to significant figures and rounding.$)$