If that s the problem then your objective will work you can tie the sink drain to the washer drain.
Tie washer drain into sink.
But i assume from your question that sink doesn t have any drain.
The size of a drain line for a small bar sink.
The washing machine drain 1 5 would run horizontally along wall pick up the lavatory drain still 1 5 and wye into a 2 drain with the shower which then wyes into a 3 drain with the toilet and on to a sump.
If the utility sink was properly installed it has its own drain.
The sink drain and the washer drain connect below the floor.
Do not connect it directly to a drain stand pipe unless the pipe is at least 2 inches in diameter.
Other options for washing machine drainage in garage.
Something like this or this but in reverse.
Connect the washing machine to the sink drain if.
Do not tie it into the trap.
This is where you will place the new y fitting that will separate the washer s drain from the utility sink s drain in the next.
Washer drain hose to utility sink.
Locate your existing washer s drain line specifically where it goes down into the floor or wall.
This install is in a basement so it would be very difficult to cut more concrete or run a separate line to the sump.
Using your utility sink s drain line measurement measure up from the ground and make a mark on your washer s drain line.
If possible and applicable note.
The drain hose from the washing machine is hung on the edge of the laundry sink.
1 install the drain hose into an installed 2 diameter drainage stand pipe.
Laundry sink waste ties in below the standpipe tie in.
There are three rules.
Water is drained from the washing machine directly into the sink.