Average transit vehicle speed: The following formula71 can be used to approximate the average transit speed S of a public transportation vehicle: Here C is the cruising speed in miles per hour, D is...

Average transit vehicle speed: The following formula71 can be used to approximate the average transit speed S of a public transportation vehicle:

Here C is the cruising speed in miles per hour, D is the average distance between stations in miles, T is the stop time at stations in hours, a is the rate of acceleration in miles per hour per hour, and d is the rate of deceleration in miles per hour per hour. For a certain subway the average distance between stations is 3 miles, the stop time is 3 minutes (0.05 hour), and rate of acceleration and deceleration are both 3.5 miles per hour per second (12,600 miles per hour per hour).

a. Using the information provided, express S as a rational function of C.

b. As a rule of thumb, we might use the cruising speed as an estimate of transit speed. Discuss the merits of such a rule of thumb. How does increasing cruising speed affect such an estimate? (Suggestion: Compare the graph of the given rational function with that of the graph of S = C.)

c. What cruising speed will yield a transit speed of 30 miles per hour?