In the kitchen there are two sinks side by side which share a common drain. One sink has a garborator. It drains ridiculously slowly. The other sink drains faster but I've been told it doesn't actually because it has more space underneath for the water to go so it only appears to drain faster, or something like that. The garborator is basically never used. Is there anything I can do to speed of the the draining of the sink(s)? I'm not sure if it's relevant but I think the gorborator is broken or doesn't work well.
Both compartments of you sink will drain through the garburator. If you do not use the garburator periodically, the drain time will get longer over time as the larger solid waste chunks will accumulate within the garburator restricting the flow. Running the garburator periodically will remove this restriction. (This can become a big issue if you have a dishwasher connected as if the drain flow rate gets lower then the dishwasher's pumped flow, water can backup the sink and overflow to the counter/floor).
If the garburator does not turn on when you flick the switch, check that the breaker is ok. Then check if the garburator has become stuck (there should be a way of manually rotating the blade from the bottom of the devise, check you manual). If the gargurator is truly broken and you plan to never use it, you can replace it with a standard P-trap.