The capacity of a highway is suddenly reduced to 60 percent of its normal capacity due to closure of certain lanes in a work zone. The flow upstream of the work zone is 80 percent of the normal capacity of the highway. The Greenshields model describes the linear relationship between speed and density on the highway, the jam density of the highway is 112 vpm, and the mean free speed is 64.5 mph.
a. Determine the normal capacity of the highway, the capacity of the highway upstream of the work zone, and the capacity within or in the vicinity of the work zone.
b. Determine by what percentage the space mean speed at the vicinity of the work zone will be reduced compared to what it is upstream of the work zone.
c. Determine by what percentage the density at the vicinity of the work zone will be increased compared to what it is upstream of the work zone.