To leave; depart, esp very precipitately: When I got back to the flat, you had burned rubber out the back
[1970s+; fr the scorching of tires in the fast acceleration of a car]
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with burn rubber
Drive very fast, as in We'll have to burn rubber to get there in time. In this bit of automotive jargon, the rubber refers to tires that heat up when they rotate suddenly at great speed.
[ ; mid-1900s