Some of the things you mention don't jive with a Collegiate.
27" tires would be wrong with a Collegiate three speed. First, I never heard of a Schwinn three-speed hub laced to a 27" rim. That is very odd. Normally, it would be on a 26" X 1 3/8" rim.
a 27" tire won't fit on a 26" rim, so... I can only guess that someone changed out the wheel which would have been enormous work - especially on the rear wheel. Are you sure that the 27" wheel isn't just on the front? IF yes, I am going to guess that they just disconnected the front brake somehow and didn't bother with the complexity of changing the brakes.