I have a washer machine in my basement that drains into my utility sink. I am finding food particles etc in my utility sink which makes me think that there is some sort of blockage and when the washer drains it backs it up into my sink. I have a bathroom right next to the utility sink and that seems to work fine. Is it safe to assume that there is a partial blockage that gets exacerbated when the washer dumps so much water but is not noticeable when simply running the faucet in the utility sink? If so is the best option to try to snake the drain?

Thank you for any advice.

". Is it safe to assume that there is a partial blockage that gets exacerbated when the washer dumps so much water but is not noticeable when simply running the faucet in the utility sink? If so is the best option to try to snake the drain?"

Not only safe but accurate. Snake the washer drain line from the roof vent. Put out enough cable to reach the base and 20 foot more. If you can't get to the roof then snake from the washer stand pipe. Work your way around the trap and put out 20 feet. Cycle the washer to test. Good luck. Tom