Does drinking alcohol faster get you drunk faster?

last night i was partying with some friends and they were drinking fairly fast chugging down alcoholic beverages on after another by their third cup they were almost drunk and cup number 4 put them over the edge while i was drinking the same thing but i was drinking much slower by my 3rd cup i was tipsy but not drunk at all... by the end of the night my friends were both head in the toilet while the effects of the alcohol was slowly wearing off on me does the speed at which they drank have anything to do with how drunk and sick they got?