Is there any way to make a sink connected to a garborator drain faster?
I would just remove the garborator if it is unused.  Over time, it will become clogged since it's internal holes are smaller than that of a normal drain.  You could try cleaning it out by throwing some lemons in it and running it for a while.

Your real problem may be a clogged drain though.  In the good drain, fill the sink completely and let it drain.  If it becomes slow at any point, you need to have the drain cleaned.