A queen wins against a rook unless there is a stalemate defence or the queen is lost. This is Philidor's position. White wins by a zugwang manoevre
1.Qe5+
Ka7
2.Qa1+
Kb8
3.Qa5
the rook must now abandon the king
3...Rb1
[3...Rh7
4.Qe5+
Ka8
5.Qa1+
Kb8
6.Qb1+
]
4.Qd8+
Ka7
5.Qd4+
Ka8
6.Qh8+
Ka7
7.Qh7+
*