I would blockade the pawn with your rook. Then bring your king in attack the pawn too and win it. After you trade rooks, push the a-pawn. Black's king runs over there. You run your king to his kingside for an easy win. Your outside passed pawn should be a big advantage. If he refuses to trade rooks, put your rook behind the a pawn and paralyze his rook, and go after the kingside.
rook and pawn endgame (sort of)
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You should play 1... Kc7 (to blockade the pawn with your king). The ending should probably be a draw.
AndyClifton is right, ShadowStar is wrong.
Play 1...Kc7, 2...Kd6. It is essential to keep your rook active.
If White attacks any of your pawns, try to counter attack one of his, rather than protecting your pawn with the rook.
If the White king goes to the king wing advance your a-pawn and you might even get winning chances.
I'm quite sure that Black can hold this endgame.
What do you guys think about this endgame? I think that white is better because of the advanced passed pawn. I play black and I am a bit lost for moves what should be black´s plan to save the game? (btw. it is not a game in progress)