Our natural red oak hardwood floors are 11 years old. The kitchen floor (315 sq. ft.) is showing some grey spots and grey streaks. An internet search concluded that the most appropriate way to get rid of the grey areas is to sand the entire kitchen floor down to bare wood and re-polyurethane. I plan on using oil-based poly. The formal living room (405 sq. ft.), which adjoins the kitchen via a 37" opening, gets very little use. Consequently, it's hardwood floor shows no wear. If I 1.) sand the kitchen floor to bare wood and polyurethane and 2.) screen and re-coat the living room floor, what is the chance that the color and sheen of the two adjoining rooms will match up? I hate to sand the living room floor to bare wood when it's finish is in excellent condition. Thanks for your help.

The only thing that will match completely, or very close to, between the floors is the gloss level, if you apply a nice film thickness to the kitchen floor.
Sanding to bare wood in the kitchen will take off the old finish which has yellowed and influences the color. Sanding the wood to any extent will expose fibers that have not been exposed to light. With red oak the sanded floor in the kitchen will be more pinkish, however the red pigment is fugitive and will bleach out in strong light fairly soon.
It should be close enough to be acceptable to most people. Be careful to stop the
sanding neatly at the edge of a strip.

Pete,
Thanks for your advice. I'll give it a shot and sand the kitchen to bare wood and just screen and re-coat the living room and hope it comes close to a match where the two meet. You said "Be careful to stop the sanding neatly at the edge of a strip." The hardwood strips run lengthwise through the doorway opening from the kitchen into the living room. The best I can do is try to sand a straight line across the hardwood strips at the doorway opening between the two rooms. Any suggestions on how best to do that? The only thing I can think of is to run a strip of masking tape across hardwood flooring strips at the doorway opening.

Since there is no floor joint between rooms I always recommend that you sand into the other room where there is a natural stop. This may be under a table or rug, or sand clear through to the opposite wall.
This will definitely look better.
Tape off the edges of the boards to make an alley. You will be much happier.
The boards may be different colors next to where you stop on the edges, but this will allow a match with the newly sanded part.
Clean the board next to where you stop and coat over the existing finish. You may not need to re-coat the whole room if the gloss level is close. You can always coat both rooms in a few years when the kitchen gets worn a little.