Good point! But here's my thought on this exercise in particular...
Cop pulls you over because you were driving above the posted speed limit. S/He might say, "Here's a ticket, and you'll have to pay a fine, because you were going TOO fast."
Here, "too" definitely means faster than you should have been, given the speed limit. Whatever your speed was, it might or might have been VERY fast, depending on the reasonableness of the speed limit.