$2.)$ A two$-$lane street on the LSU campus is subject to periodic stoppages for student crossings. Among the

concerns at this location is that traffic waiting for pedestrians could back up and block another crossing

$1,500$ feet prior to the subject crossing. To decrease the likelihood of such a condition, you have been asked

to assess if a pedestrian crossing signal that limits the time that students are permitted to cross will help.

To assess the situation, you make measurements of traffic conditions on the street and find that drivers

typically maintain average time headways of $7\mathrm{.}8$ seconds at the posted speed of $25$ miles per hour. Next,

you note that vehicles stopped for students, typical maintain an average spacing of $10$ feet in between

vehicles and once everyone passes drivers depart from the crosswalk at $15$ miles per hour with a spacing of

$50$ feet in between vehicles. Finally, you determine that, based on the traffic mix of trucks and cars, the

average length of vehicles on the street $28$ feet.

Based on these conditions, and showing all of your work and proof of your answer, what would be the

maximum time $($in seconds$)$ that you would recommend for the pedestrian signal to let students cross

without causing vehicles to block the adjacent upstream crossing?