[hughc]

I'm assuming the drain from the kitchen sink and washer join at some point. I had a similar problem two weeks ago where the drain from the kitchen sink and the sink in the nearby washroom were both backing up. In my basement (under the kitchen floor) I was able to see where these drain pipes joined onto the main drain pipe. (The large 5"pipe) Fortunately I was able to separate the sink drains from
the large drain pipe. The pipes were clogged at that point and I am assuming it was mainly from too much use of the garbarator and not enough flushing afterwards. Regardless, it was plugged so with a couple of tools ( 12" pry bar and snake) I was able to clear most of it away. I poured a generous amount of draino into that joint area and let it sit for 30 min or so.
Screwed it all back together, flushed it all with copious amounts of boiling water and it hasn't given a problem since.
In retrospect I suspect somebody is pouring a bit too much fat or bacon grease thru the garborator.
BTW, my house is over 70 yrs so plugged pipes can be expected.