The kitchen sink backs up, or both sides fill
Grease and food scraps go down warm, cool in the line and stick, a layer at a time, usually past the trap where the pipe runs into the wall. If the dishwasher drains through the sink, it backs up there too.
A sink clogged at the trap is our $99 sink drain clearing. Past the trap, it’s one drain cleared, $200 to $800. Grease that comes right back after a cable is a job for a water jetter.
