Douglas Harper's Etymology Dictionary
rat-race
also rat race, 1934 in reference to aviation training, from rat (n.) + race (n.1). Rat-run is from 1870 in a literal sense.\n\nA rat race is ... a simple game of "follow the leader" in fighter planes. The leader does everything he can think of -- Immelmanns, loops, snap rolls, and turns, always turns, tighter and tighter.
["Popular Science," May 1941]
\nMeaning "competitive struggle" is from 1945.Wiktionary
rat-race
vb. To rat run, that is, to drive on side streets, often at high speeds, to avoid traffic.
Usage examples of "rat-race".
Well, I write this a long time later, and Singapore, that elegant rat-race, has now gone its own way, free of British control.