Bathroom Extract Fans

In the renovation project which is our house, I have two bathrooms (one directly above t'other) and need to install 2 extractor fans (and ducting). There is already a hole in outside wall of downstairs b/room, so I want to duct the upstairs one to it and "tee" into this ducting for the the downstairs one. Is that gonna work ? Anyone done that ? Your quick replies are appreciated, as the smell is getting too much !

don't eat so many beans or brussel sprouts

I would say no because one fans out put will blow into the others outlet, that said you can get fans with non return wind flaps, but i still do not think it will be all that good

OK Thanks for that.