Clearly write equations $($as you may need to use$)$ while solving a problem

Mention proper units. Points will be deducted if units are wrong or if you do not

mention those

Q$1.$ In a school zone, the traffic flows and speeds of vehicles are observed in three sections:

Section A $($Upstream$)$: The vehicle flow is $1,550$ vehicles per hour, with a mean speed of

$40$ miles per hour.

Section B $($School Zone$)$: The vehicle flow decreases to $1,350$ vehicles per hour, and the

mean speed reduces to $25$ miles per hour.

Section C $($Downstream$)$: The vehicle flow ifficreases to $1,515$ vehicles per hour, with a

mean speed of $35$ miles per hour.

The length of the school zone is $0\mathrm{.}6$ miles, and the zone operates for a duration of $30$ minutes.

Based on this information, calculate the following:

The speed of the shock waves between Sections A and $B$ and between Sections $B$ and $C.$

$(15$ points$)$

The length of the queue formed after $30$ minutes of operation. $(10$ points$)$

The time required to fully dissipate the queue formed after $30$ minutes. $(15$ points$)$