Pawn Rook Vs. Rook

That all depends on where the pieces are on the board. For example, the Lucena Position is a win for the side with the pawn, however other positions allow such ideas as the Philidor Draw and other methods. There are many different examples.

A great way to learn about rook and pawn endgames is to become a diamond member of chess.com, and view the videos on such matters. To date, there are no less than 10 (!) such videos, all by FIDE Master Daniel Rensch.

Where must the pawn be (only one)? Middle, side...etc.?

It's not just the position of the pawn that matters, it also depends on where the kings and rooks are.

Actually, his question as posted of rook+pawn vs. pawn is almost always a win (there are a few exceptions where a piece can be immediately captured, maybe promoted, but in general it's a win). If however you mean pawn + rook vs. rook then Nytik is right.

Actually I found the title very confusing. An example of non-confusing would be Pawn + Rook Vs. Rook. Furthermore, you actually titled it Pawn Rook Vs. Rook. Basically, there's no such thing as a pawn rook, so your title is nonsense and not clear at all. I assumed you meant a rook pawn, which means a pawn on either the a- or h-file, but you could also have easily meant Rook + Pawn. Also, what you wrote in the first post disagrees with all of these interpretations. So what you posted was actually nonsense, not what I posted.

Basically, if you want to be really clear, post a position.

Pawn + Rook vs. Rook endings are a really good entry point into studying endgames in general. They aren't ferociously complicated (like some two piece vs two piece endings are) but they aren't "oh it's always a draw"  either... There are some good tutorials here, on you tube, and elsewhere on these endings. Start with the Lucena postion (most tutorials will teach the Philidor postion along with it, they go together... Lucena is a "pawn promotes for the win" technique, and Philidor's is the "pawnless side perpetual checks for the draw" technique. Master those two ideas and you've got the foundation of pawn and rook endings.

jeremy silman's endgame book teaches this stuff quite well, also IMO.

K R P vs K R

Here we see the red king has been pushed to g8. The blue rook is delivering the check before mate. The red rook must come to f8 to block and then R x R checkmate. So this example is not a draw.

Yes, but generally, now that I understand what you are talking about, R+P vs. R is a draw. The generally depending usually on the ability of the defender's king to get in front of the pawn and to stop the pawn from hitting the 7th rank. It's based on the Philidor position, and called the 6th rank defense.

 No problemo! BUT yeah the kings are at risk from enemy rooks like Wandering Winder points out.

You're rated 2605 in correspondence chess... and this is your understanding of rook and pawn endings? I guess you're so strong in the middle game you just never get to endings.

The technique is to get your rook to your third rank (his 6th) before his pawn or king get  there... your rook walls off his king from the third rank and the only way for him to cross it is to push his pawn to use as a sheild...  at which point you bring your rook back to your seventh or eighth rank and subsequently check his king, forever.... he will have no way to avoid your rook checks.

Glad its not just me...I was like...its late but that's definitely not supposed to happen :o

Yes ... very interesting moves, there.

The white king taking his own pawn is

a brilliant stroke.

regarding the moves whis put out...

"Yes... that's it... and then... yes... wait. no not there, hunh? NO!? Whaaaaaat?!"