Definition of rat-race:
(v) :
(slang, intransitive, idiomatic) To partake or participate in a rat race, in all senses.
(v) :
(slang, transitive, intransitive) To rat run, that is, to drive on side streets, often at high speeds, to avoid traffic.
(n) :
Alternative form of rat race. [(informal) An activity or situation which is congested with participants and which is hectic or tedious, especially in the context of a busy, modern urban lifestyle.]