Highway tunnel traffic (two parallel lanes in the same direction) experience indicates the average spacing between vehicles increases with speed. Data from a New York tunnel show that between 15 and 35 mi/h, the space x between vehicles (in miles) is x = 0.324/ (42.1 − v) where v is the vehicle’s speed in miles per hour.
(a) Ignoring the length of individual vehicles, what speed will give the tunnel the largest volume in vehicles per hour?
(b) Does including the length of the vehicles cut the tunnel capacity prediction significantly?
Assume the average vehicle length is 10 ft. (c) For part (b), does the optimal speed change much?