A field-and-track man run 100 yards dash in 9.3 seconds, but the judge give him 9.4 seconds saying "We have to go with the higher time". What exactly does it mean?
The time is a number of seconds so, in this case, "the higher time" means "the bigger number of seconds". "Go with" means "use" or "choose". So the judge is saying that, given the choice of using 9.3s or 9.4s as the athlete's time, they have to choose 9.4s. (I'm not sure what the context is that means they have to do this.)