Why is dirt backing up in my kitchen sink when my washer drains?

You have a partial blockage in the horizontal drain line in the wall that won't allow the water drain. The solution would be to dip the water out of the sink and remove the "J" bend from the trap and snake the drain line, (see image). You will run into a 90 degree bend about 8 inches in but once around that you only have to put out 6 more feet of cable. After, flush with hot water, Good Luck.

John

The drains are probably not vented right or a clog. When you drain water from above and the water backs up it will push through a lower drain as the air and water slightly pressurize the drainage pipe. So it's a partial clog or no or improper venting or the roof vent got clog by tree debris or snow ans ice. Check roof vent' How long has this problem been going on and did you try to plung at all?

Signed 21 boat

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why is dirt backing up in my kitchen sink when my washer drains?

I don't think the clog's located in the sink drain in the wall. Dirt in the back up water makes me wonder if you don't have a crack or opening in the drain line downstream from the kitchen sink. Send a snake down the kitchen roof vent to clear the blockage. Put out enough cable to reach the base and 20 feet more. If the auger comes back with dirton it I would consider sending a cameria down the pipe to check for a break in the line. Good luck, Tom