Basement washer drain connection to existing floor drain
I am on city service. I would like to connect my basement washer drain into the existing floor drain (3" line). I cut the line about 3 feet down from floor trap and installed a 3x2inch y. This existing floor drain takes a 45 turn about 6" down from where I cut it. The 2 inch will drain the washer . I connected a 2' drain pipe, to the y, about 3 feet long for the washer to drain into. Before I connected a 2' cleanout where the pipe would come out of the floor, I tested the system using a hose sending water down the 2" drain. What happens is the water does drain, but it also backs up to the floor drain for some reason. There is a about 1/8 to 1/4" slope on both the 2" and 3" pipe. The floor drain trap does not fill any more than the height of the 2" pipe where the hose is sending water. I'm worried that if the washer were to drain, I would get suds comimg up the floor drain.
Any ideas would help.
Thanks...