Traffic flow Cars are crossing a bridge that is 1 mile long. Each car is 12 feet long and...

Traffic flow Cars are crossing a bridge that is 1 mile long. Each car is 12 feet long and is required to stay a distance of at least d feet from the car in front of it (see figure).

(a) Show that the largest number of cars that can be on the bridge at one time is where  denotes the greatest integer function.

(b) If the velocity of each car is v mi/hr, show that the maximum traffic flow rate F (in cars/hr) is given by .

EXERCISE