During the spin cycles, when gallons upon gallons of water are getting purged from my washer into the draining sink next to the washer, the water has started coming out of a drain in the floor of my basement in between my washer and dryer.

It looks like it's supposed to be going up out a couple of exit tubes but they don't seem to be able to handle all of the water at once. I'm thinking part of it has to do with me not replacing the lint catch over the end of the drain hose from the washer and that it's likely backed up a little.

Is there any way to flush that system out without flooding my basement again?

Am I on the right track?

Thanks,

-Legs

The sink drain and floor drain are connected under ground. Therefore, they'll become one drain. You have a clog in that common drain, someplace under ground. You need to snake this drain.

You need to snake this drain. Milo's correct. He just didn't go far enough. You have a blockage downstream from the floor drain. This can be done from one of two places.
1) From the floor drain,(see image). You can work a 3/8th inch snake past the trap or if it has a cleanout plug, as shown, you can snake from there
**or**
2) You can snake from the slop sink roof vent. Put out enough snake to reach the base and 20 feet more. Good luck and thanks for rating my reply. Tom