Traffic flow on a section of a two$-$lane highway can be described by the Greenshields model, with a mean free speed of $56$ mi$/$h and a jam density of $146$ veh$/$mi$/$ln$.$ At the time when the flow was $90$ percent of the capacity of the highway, a large dump truck loaded with heavy industrial machinery from an adjacent construction site joins the traffic stream and travels at a speed of $12$ mi$/$h for a length of $3\mathrm{.}5$ mi along the upgrade before turning off onto a dump site. Due to the relatively high flow in the opposite direction, it is impossible for any car to pass the truck. Determine how many vehicles will be in the platoon behind the truck by the time the truck leaves the highway.

$\_\_\_$vehicles