Upgrade from Mac OS X 10.6.8 "Snow Leopard" to OS X 10.10 "Yosemite"; App Store takes over 20 hours
If the desired Mac is slow, you can always use another Mac to do the download of the OS X installer.


Make a guest account on that Mac and sign in with your AppleID since you'll want to shift off your boss's password and get everything under an ID you control.
Go to the App Store and download the installer - but don't run it.
Copy that installer application to a USB drive and take it to the slow mac.


The slow Mac probably needs a back up and possible Disk Utility to repair the catalog structure. 

Worst case, you can order a USB media from Apple - call in to the sales number for your country and ask to purchase a media instead of a download. They often will help you enough to get your Mac upgraded for free.

Once you get the install running, you can look at /var/log/install.log to see the progress and where things get slow or hang.