Pawn Rook Vs. Rook

 Well, both players are rated 0, presumably they don't know how the pieces move! I like 4... Ra1!! That would make Kasparov fall out of his seat...

 Re-read your question. It does not say the same thing as the thread title.

 No, a pawn and a rook is almost always a win against only a pawn with perhaps a few exceptional cases.

Have you tried the computer work-out feature here on chess.com? That explains Lucena, Philidor, and all sorts of other things like that.

:))

 Philidor was one creative player...combining rook and bishop moves in one and forcing his opponent to take his own pawn.  Simply brilliant. 

Yes, that's how you do it, but where your rook is once you reach R+P vs. R is not so important generally as it can get into position quickly. More important is your king's position as you can never stop them from getting this far if your king is out of position. Eventually both king and rook need to be in place, but whether this can happen is based more on whether your king can get there or not, as the rook nearly always can, and even when it can't there are some cases where the weaker side can draw anyway, though with much more difficulty. And as his question was when it's a draw, this is what I answered. I actually pride myself on endgames, though they aren't as strong as they could be. My rating is as high as it is because a) I haven't played many games but the rating system on this site has your rating jump around very quickly and b) I actually usually win out of the opening.

Not if your opponent played correctly.

EDIT: That's assuming that black is moving up.

I agree, mostly... the first time I read it I misread/read too quickly and thought you were saying R vs. R+P was simply drawn -- which you didn't say and which it isn't. Yes, the King's position is most important. But I do think it's not fully correct to say the King on the back rank is what stops the pawn.  The King doesn't do it by himself... yes you're right the rook is less critical because it get usually get into position quickly, but that assumes the player knows where the rook is supposed to go! If the rook is misplayed there's mate threats and tactics which can blunder the game away. I'm sure you know all this, but you didn't say it!

That position you have there is drawn, and is not the beginning of the endgame. To properly play endgames, you need to know the basics to play correctly. Had you known this position was a draw, you wouldn't have wanted to play 41...Rxh5. Instead you should have played 41...Re3+ followed by 42...Re6. From this position you should be able to keep your two pawns and win his and go onto win that endgame. 

Well that position is a draw anyway, but I wouldnt be looking to swap the rooks off in that position as in this case that leads to an even more clear cut draw.  Usually the side that is worse wants to keep the rooks on, but here the king and pawn endgame is simply drawn, and is much simpler. 

 It's very surreal : as chess board as well position.

....umm....great non-mistake play by black....(sarcastic)