Renovating an old farm house. We have a room at the entrance that is 9x22 running from the front of the house to the back. Our plan is to divide it so that the front is a 9x10 mud room and a 9x12 office in the back. There was already a 6 inch flex duct on a 4x10 register in the back. If I use a Y on this duct to first supply the office, then run the other branch to the mud room, is that a viable approach? Maybe reducing the short line to the office register to 4", then keep the longer run to the mud room at 6" might help equalize the duct pressure? Any thoughts?