A continuous segment of a highway has two flow regimes, as seen from a satellite image. The upstream regime has density of k$\_1=90$ pc$/$km$/$ln and the downstream regime has density of k$\_2=45$ pc$/$km$/$ln$.$ It is impossible to estimate volume and speed from one satellite image. Assume that a highway$$s macroscopic traffic flow follows the Greenshields model, with u$\_$f$=90$ km$/$h and k$\_$j$=125$ veh$/$km$/$ln$,$ estimate $($a$)$ the speeds and volumes of the two regimes, that is$,$ u$\_1,$ q$\_1,$ u$\_2,$ q$\_2$; $($b$)$ the speed and direction of the wave front that separate the two regimes, that is$,$ u$\_$w; and $($c$)$ Sketch by hand a plot of the q$=$f$($k$)$ curve with the two data points $($k$\_1,$ q$\_1),($k$\_2,$ q$\_2).$