Adding Utility Sink in the Garage

[willkazan]

Dear everyone,
I'm new user and this is my first time using a forum, I hope that I learned how to use it correctly.
I'm planning to install a utility sink in the garage but I have some doubts about the drain and vent in the image below.

Behind the garage wall is the living room and the temperature never reached below 42F in the winter.

The PVC pipe comes from the washer machine upstairs and goes to the basement downstairs.
According to the PA code maximum distance from P-Trap to Vent is 6' with 1/4" each 12" slope which I'll have a 3' 8" of length with almost 1" of slope, but I'm not sure if can use the same drain pipes that comes from washer machine without another vent pipe exclusively to the utility sink. Is that possible?
In case if is not possible, can I use an AAV or maybe a connection in the middle of the sink drain to any point higher to the drain pipe?
Thank you very much in advance.

 

[Reach4]

According to the PA code maximum distance from P-Trap to Vent is 6' with 1/4" each 12" slope which I'll have a 3' 8" of length with almost 1" of slope, but I'm not sure if can use the same drain pipes that comes from washer machine without another vent pipe exclusively to the utility sink. Is that possible?
In case if is not possible, can I use an AAV or maybe a connection in the middle of the sink drain to any point higher to the drain pipe?

Use the AAV if using IPC. Maintain 1/4 inch per foot of slope until the AAV. After that, you can go steeper.

If you wanted to use a real vent, you would have to bring that down from the floor above, because your proposed vent carries drainage from above.

 

[Sponsor]

 

[willkazan]

Thank you Reach4! Now is much clear!