Water from both washing machine and DW?

Hi, over the last couple of weeks we had a problem with thewater in the kitchen sink draining away vercu slowly. I used a chemical and it was fine, unfortunately it would seem the problem is with the washing machne and possibly the dishwasher, when the the WM empties on the spin cycles the water is going in to the sink, there are remnants of food which infers the waste water from the WM is some how coming to the sink via the DW. Help....