A nice problem. To really figure this out quickly, you have to be aware that the game is won even if white's king is on a7 and the black pawn is on f4 with black's rook sacrificed for the a-pawn on a7. This leads you immediately to 1.Kb6 to escort the pawn to a7. White has time to catch the f-pawn since black will have to move the king down the board, too, to protect it from the white rook.

Of course, you also have to realize that you can't win with 1.Rb8 with the intention of 2.Rb7- black will just put his rook on h8 and then a8.