The way I've seen it handled in the past isn't to divide the rent - since, as a PP noted, those who are paying higher rent tend to feel more entitled to the common areas - but to divide household responsibilities based on who has the better room. So, whoever had the best room usually was responsible for buying toilet paper and paper towels, doing the "heavy" cleaning like mopping the floor when it needed it or scrubbing the tub (although each girl was still responsible for her own messes, like dishes) and coordinating utility payments/repairs with the landlord/various other tasks related to the apartment. Obviously contingent on each girl not abusing the system, like using vast amounts of paper towels or tracking mud all over a floor.
I'm going to go against the grain and say I don't think it's fair to divide rent based on who has the best/worst rooms. Each girl agreed to the apartment at the rent that it was advertised at, and what if more than one girl would rather take the little room for cheaper rent? I wouldn't be happy to be apartment searching and suddenly find out I needed to pay more than a housemate based on drawing lots. To me, equal rent = equal rights to the household, and messing with that formula is asking for trouble.