1. To participate in a contest of speed: There are seven horses that will race for the championship tomorrow.
2. To go, to move, or to function at a very fast speed: Fern's heart was racing because of the speeding car that almost ran into her own car.
3. To try to do something very quickly because there is not much time left to finish it: Jennifer was racing against the clock to be sure that her class assignment was handed in on time.

Patricia and Alisa overslept and so they had to race like mad to get to school on time and avoid being tardy.