A traffic engineer has set up a one$-$mile study segment of a corridor. He measures the speed of $10$ vehicles. Calculate the space mean speed and time mean speed of these vehicles. If the space mean speed occurs at an optimal flow with a density of $75ve\frac{h}{m}i,$ what is the capacity of this roadway? $[10$ points$]$

$\backslash$table$[[$Measurement$,1,2,3,4,5,6,7,8,9,10],[$Speed $($mph$),45,43,39,52,48,48,52,46,53,42]]$