If you have a 56K dialup modem that claims to have connected at 115,000 bps (which is approximately 112K), you've run into a marketing trick. Many modems are now factory set to return the speed of the connection between the modem and the computer, not between the modems. Check your modem manual for how to change this in your modem startup code.
From
CITES's Dialup access troubleshooting
I believe you when you say you experience faster page loads and all, you should! But the difference is not from 36,000bps to 115,000bps.
36,000bps to 45,000bps is actually not bad for a 56K modem, but I accept no less than high 40s to low 50s.
The chances are your modem is operating at its best at around low 50s.
Assuming you both have the exact same computer, the reason for different connection speed and/ or surfing speed would be your roommate's Modem, configuration and/ or drivers. If you were to put your modem in his/ her system, things would be the other way around.
Even if both modems are the same, his/ her system, configuration and setup as well as presence of any malware or virus could cause different results (mainly in surfing)
One other factor is the phone jack, assuming the system’s configuration, setup, modems and drivers are identical, if a jack is defective or there is a short, that could cause different results as well but with phone lines, this should affect all the jacks connected to the same pair of wires but then again it could be the receptacle.
Assuming the OS is setup properly with all drivers (including chipset), I have seen changes in initial connection speed just by changing one or more of the following:
IRQs and ports
Configuration (initialization strings and such)
Drivers
Modem
Different cables or jacks