I am making a new thread for this rook ending. We began discussing it in the "Endgame-play" thread.

I have another ending for everyone to consider: 
White has pawns on f2, g3, h4, a6. Ke3, Ra7. 
Black has pawns on f7, g6, h5, Kf6, Ra2. 
White to play.
The position occurred in Tal-Gipslis, 1983. Tal played 1. Ra8 and the game was soon drawn. But it turns out that white is winning.   
 
There is actually published analysis on this, and I first saw it a few years ago, and spent a while looking at it. The position is interesting, because it is the sort of thing that might come up in a real game. I'll tell where the analysis is online if there is any interest. I think the online analysis even goes into whether or not the position is still winning even if black is to move, but I never got that far when I was looking at it.

As a hint, white's first move is not 1. f3.