Rook+Pawn vs Queen

 Hi everyone! I was playing this game with a Rook+Pawn vs Queen end game. I played like 30 moves but wasn't able force a win on the rook side, I was playing black, with the queen and in the end I offered a draw and white gladly accepted. I am wondering whether this position was a win-able from black's point of view. Can someone please tell me this and also how to win in such position. I tried so much but couldn't. Thank you. 

It is a win but it's very hard. Use a tablebase to show you the win. The position you show takes 32 moves to win (with best play from both sides.)

The Shredder tablebase is viewable at: http://www.shredderchess.com/online-chess/online-databases/endgame-database.html

Queen vs rook is hard enough. I wouldn't even bother worrying about this personally.

 This is a win. You must get behind the pawn with your queen and use mating and fork threats to parce the pawn from the rook. You need to force the king in front of the pawn and attack it from the side.