Studies have shown that the traffic flow on a two$-$lane road adjacent to a school can be described by the Greenshields model. A length of $0\mathrm{.}5$ mi adjacent to a school is

described as a school zone $($see the figure$)$ and operates for a period of $30$min just before the start of school and just after the close of school. The posted speed limit for

the school zone during its operation is $15m\frac{i}{h}.$ Data collected at the site when the school zone is not in operation show that the jam density and mean free speed for each

lane are $130ve\frac{h}{m}$i and $60m\frac{i}{h}.$ If the demand flow on the highway at the times of operation of the school zone is $90\%$ of the capacity of the highway, determine the

following.

$($a$)$ the velocity of the shock wave created by the operation of the school zone $($Enter the velocity of the backward forming shock wave in mi$/$h$.$ Indicate the direction with

the sign of your answer.$)$

$m\frac{i}{h}$

$($b$)$ the number of vehicles affected by the school zone during this $30-$minute operation

vehicles