We are remodeling an old house. We have an existing sink and drain (2") in the laundry room, but the sink is just a regular kitchen type sink. In the basement where the existing drain elbows up to the sink is where we want to tie into the drain system by replacing the elbow with a tee. On the new drain line will be the washer first then an elbow leading to the new kitchen drain.

Will we have problems with water backing up in either sink when the washer pump drains the washer?