It depends on how much the person had to drink, and how long ago they had their last drink.  A person’s body eliminates alcohol at a constant rate to lower intoxication levels by .015% BAC per hour.  If an average sized person has only one drink, the maximum intoxication might be about .02% BAC.  In less than two hours all the alcohol will be eliminated, and their breath alcohol test will be zero.

On the other hand, if a person drinks enough to have an alcohol level of .20%, well over the legal limit for drunk driving (.08%) in every state, it will take over 13 hours after they stop drinking for their alcohol level to reach zero.