Music Composers Unite!
I dont know if this would work but perhaps it would point you in the right direction
(this guy has a lot of great little free software so do browse around)
to solve your particular math problem
divide 115bpm by 60sec
the quarter note lasts 1.917sec
maybe i'm misunderstanding, but wouldn't the formula just be 60 divided by the tempo?
i.e: 60 / 115 = 0.5217 seconds per quarter note.