One of my failed try is attached
Two passed pawn with Rook vs one passed pawn with Rook
There seem to be a few options (probably higher rated players than me can explain it more), but from the initial position I would have set out to advance the pawn with c4. Even from your posted fail attempt I think you had it...16. Rg7+ and then trade off the rook for the pawn. Your connected passers w/ king support should lead to one of them queening.
OK, I dam care with the name, i am concerned with the plan. I am sorry, I am unable to change the title of the post. Any moderator can you please do it.
As I don't have the book and being a youth trainer:What taught the book before giving this position?
Thanks @IM pfren. I agree, I am not good in calculation thats why I am trying to learn.
Problem that I face in this game is how to stop the black pawn from promotion if i go after piece exchange. For a low rated player like me it is easy to think to go for Exchange pieces but it was not happening. Sure you can say, my bad calculation.
Two machines can do that but i don't get why certain moves have taken place. If you can do with ideas and plans, kindly help me out.
@hpmobil: The book teaches the convertion of one game to other known end games. The previously the book had taught the Rook with pawn vs Rook end games. The idea in this game was to covert to that position and that will lead to the win. The engine, ofcouse is not following the moves presented in the book as in many previous games but in them plan took me to the victory. Second, I am not good in calculation, i agree.
Ok, finally, the engine said, go and get the win and have a life. The engine exchanged the Rook for nothing :P
That's the way. Continue with a friend. Forgot which Irish author said something like: With the word 'experience' we hide how often we came off with bloody noses. (be carefull retranslation)
Found a simple plan that is most of the time working
1. if the black plays waiting move with rook and there is nothing under attack, move the pawn
2. if black rook comes under the white pawn, try to push him away using king
3. if black king try to come closer to white rook, push him away with check
4. if black rook move to upper side of board, try to support the pawn with the white rook from the bottom side of the board

When you play an ending planing is important (so is calculation) Try this following plan: Its a simple win because you can
1- cut black King from coming to the defense of the white pawns
2- bring your own king to push that pawns.
3- if black try to push his pawn you always have the option of trading your rook forit, if your pawns are advanced enought the rook by itself cant defend them.
4- win the position and have a coke!
I am studying one of the end game from the Jeremy Silman endgames course book on page 279. I am trying to play against Xboard engine Fairy-Max. According to Siliman, this position is a win for a white. I am going for the idea to exchange one pawn to get a pawn with rook vs rook end game but all the time I end up losing the two pawns that ultimately results in a draw. How do you play this position?