Chase Race Race Against Time

http://www.evilhat.com/lab/BeatTheClock.zip provides a really nice model - a layout like a clock (12 circles around a larger circle, one in the middle as a starting point) and the outcomes of in-game challenges move your “piece” forward and back around the clock. After you reach 12 you exit.

This could easily be made into a generic chase, race or race-against-time mechanic.

Inputs: Competitors; chase, race or race against time? Does each person have a clock or is there one clock for everyone?
Outputs: Chase: The pursuers catch up with the pursued, who has a head start, delaying tactics etc. Possibly multiple laps, with a possible victory condition if the pursued can get round a certain number of times without being caught.
Race: Someone gets all the way around the clock first. Possibly multiple laps.
Race against time: Someone reaches (or not) another victory condition before the clock runs out.