46 ( +1 | -1 ) There are rare exceptions, but the general result in this endgame, assuming both sides play error-free, is a win for the Queen. The technical process is very tedious and takes about 30 moves. It involves driving the king and rook to the edge of the board, then forcing the rook to move away from the king using zugzwang, then winning the rook by a double-attack. Easier said than done, of course.
75 ( +1 | -1 ) Generallyat worst, this ending takes about 25-30 moves to win the rook, well outside of the 50 move rule. In the past this ending used to be not very hard at all because the side with the rook would put up less-than-adequate defense, however, with the recent advent of computers and GM Walter Browne's famous match (where he failed to win the rook in 50 moves) has produced new analyses that can make it very hard for the side with the Q to win if they are not well acquainted with the theory.
All told, this rarely happens except in a select few GM games, and usually the side with the Q wins easily. If you want a more in-depth study of this ending, look at Nunn's Secrets of Pawnless Endings.