Maybe the easiest way to do this for you would be the either start with a vehicle that has a hall effect speed sensor already and tie in to that, or to place a magnet on a drive axle with a hall effect sensor fixed to particular point (this is probably easier on a RWD vehicle with a larger driveshaft), determine how many units of distance apply to a single pulse, build your circuit to count the pulses and multiply that by your "cab fare" for the given distance. Using the hall effect sensor and square wave allows the use of digital circuits and avoids the need of an A to D converter.
If the vehicle you choose has anti-lock brakes, you likely will already have access to a pulse from a tone ring and hall effect sensor system. The downside to this is there will be many tones per axle revolution so your counter will need to be capable of registering the tones coming in at a much higher rate.
-Rod