Using the speed in miles per hour modeled as a function of density in vehicles per mile with a Greenshields Model in the form u$=75-0\mathrm{.}682$k$.$ There is one travel lane in each direction on a two lane highway. Assume the road does not allow passing, and that there are no intersections requiring stopping etc. The vehicles are traveling with a density of $19$ vehicles$/$miles when, $20$ miles from the destination, a slower motorist turns onto the road in front of them, traveling in such a way that if there were many such vehicles, they would have a density of $30$ vehicles$/$mile$.$

If these conditions persist, how many vehicles are in the platoon behind the slower vehicle when it reaches the destination after traveling the $20$ miles?