Also, I read your last sentence as "You should work out in the library," and imagined laying down under a cart full of large hardcover volumes, trying to grunt very quietly while pressing it. Just sayin'.
The staff (and/or branch policy) ultimately decide what to do if a group of people is obviously using the library as a kind of temporary office, and they may request you make more formal arrangements. (The branches I worked at always had back rooms that could be rented out to tutors.) With several people, noise may be an issue. Still, one person typing, or two or three people working with occasional quiet collaboration is probably on par with a couple teenagers studying together. Just be considerate.
Libraries are paid for with tax dollars, and (as tptacek noted) staff are generally more nervous about empty libraries. Branch funding is often closely tied to usage stats - people coming through the door each day, circulation, internet station sessions, etc.
Also, depending on the neighborhood, the staff are probably more worried about drunk and/or mentally ill street people, misbehaving teenagers, etc. (Oh, the stories...)
* Great job to have through college, BTW.
Two things to realize:
(1) The library staff is a lot more nervous about the library being empty than they are about it being full. Something about busy libraries being the reason they get paid.
(2) If libraries have headache clientele, it's the homeless. I had no idea what a mess that situation was until I started going to the library every day.
This I can attest to.
At our local public library there's a lady who is constantly picking up and re-shelving kids books only to have some kids take a bunch out and toss most of them on the table or the floor.
When I asked her if she wasn't frustrated, she said counter-intuitively that she's actually happy to come in to the section and find a ton of books to re-shelve.