The length of time that 3 beers will stay in your system depends on how much beer is in those 3 beers.
If you drink three 12 ounce beers then those 3 beers would stay in your system for 36 hours before they fully leave your system.
To figure out how much beer will stay in your system for how long figure on the beer will stay in your system for 1 hour per each ounce of beer.
So a 12 ounce beer will stay in your system for 12 hours but it starts leaving your system within a few hours.
So if you drink 3 beers then you should avoid driving or operating any machinery for at least 2 to 3 days to allow the beer or alcohol to leave your system.