This is the Philidor Position in the Queen versus Rook ending, not to be confused with the Rook and Pawn ending by the same name.
It is possible to play the ending out on this website, which tells you the best moves on the righthand side.
This ending is normally thought to be quite difficult, but this is one of the critical positions and it is fairly easy if you know what to do. (The other critical position is called the 3rd rank defense, and it is harder.)
White easily wins is with a triangulation after 1. Qe5+ Ka7 2. Qa1+ Kb8 3. Qa5 arriving at the starting position with it being Black to move instead of White to move. Now Black is forced to move his rook away from the king. Then White can check the king until he is able to fork the rook.
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