The K+Q side has to avoid a stalemate, for instance if black is to move
he simply plays Rd6+ (QxR = stalemate).
Apart from that, the queenside should win in 20 - 30 moves. Gradually moving the kings closer to each other (the rookside king close to the border, later on to the corner). With mating threats, force the rook to move away from his king, and then, still with mating threats, find double attacks on king and rook. Given the theoretical maximum number of moves, you can afford a few tries (but not allow stalemate) and still win in time. It is not very difficult.
Here is a setup game where I guided (through messages) my opponent towards the win.
Game 845538
Originally posted by Mephisto2Well, that was nice of you 😛
Here is a setup game where I guided (through messages) my opponent towards the win.
Game 845538
Yes, white can always win Q vs R except in the rare instances mentioned. But it's very difficult. GM Svindler played a game in which he had a lone queen against his opponent's lone rook and was unable to win within 50 moves and the game was drawn.