My uncle told me stories about living in rural Michigan, and how the first thing that people did when a road got paved in the area was set up a quarter mile marker.
A dragstrip is a facility for conducting automobile and motorcycle acceleration events such as drag racing.
Although a quarter mile (1320 feet, 402 m) is the best known measure for a drag track, many tracks are eighth mile (201 m) tracks, and the premiere classes will run 1,000 foot (304.8m) races
But honestly, why these lengths specifically?
Many short races, for feet or horses, that started way back when are some number of furlongs.
Right next to the parsec, but only because of the Star Wars references :-)