When I was in this situiation,I thought it will be a draw.No helpfull reference I could find in this site.I played it with fritz ,but when I had queen it easily cracked and didn't make good moves.
Then I invented some principles for myself and I could win in 35 moves.
- Move the king as near as u can to the opponent's king In a way that he can not check u with the rook.
- With the big plan of restricting the king, move your queen too.Sometimes checks with queen is good,although he would defence with rook because the other advantage will happen after that.
- Checks from his rook to your king if produces advantages,are welcomed.
- You should gain a position like 95th move.Then checkmate in all variations is possible.
If You Don't lagh , I should say that my theory says that if he want to resist from going to 95th position and you have done through the instructions you will have the match with a fork.