On-line Math 21

4.1  The Mean Value Theorem

Example 2 My commute to work involves a stretch of the Northeast Extension of the Pennsylvania Turnpike. I get on (at Plymouth Meeting), mile marker 20, and am handed a ticket, with the time stamped on it. When I get off, at the Quakertown exit, mile 44, 21 minutes later, the ticket taker hands me my change and a speeding citation. Have I been wronged?

Solution

Since the elapsed time of my travel between getting on, and getting off, the turnpike was only 21 minutes, and yet I travelled 24 miles, according to the MVT at some time t = c my speed v(c) along the road was

v(c) = 44-20 21-0 = 68.57mph.

No, since the speed limit is never more than 65 mph I was speeding and deserved the ticket. I wouldn't have much sympathy in court, either, since half of that portion of the road has a 55 mph speed limit.

Don't think that this sort of automatic ticketing can't happen.

Copyright (c) 2000 by David L. Johnson.