Usually you shouldnt draw because it is really easy to fork your opponents king and rook
Queen vs. Rook & 2 Pawns Endgame
These positions are rarely lost for the K + Q side, but they can be drawn in many cases. The most common involves a "fortress" where black's pawns are connected, ideally chained, with one of them defending his rook and his king is close enough to guard the more backwards pawn. In that situation white can check perpetually, but he can't gain a tempo or do anything to force the rook away from whatever rank/file it's controlling. With white's king unable to make the necessary inroads, mate is impossible.
Usually you shouldnt draw because it is really easy to fork your opponents king and rook
Even without the pawns, K+Q vs. K+R can be one of the hardest in the book if the R is next to the K.
@DrFrank - can you post the position?
I would say to NEVER accept a draw in this position. You can easily get at least 1 pawn with the teamwork of your queen/king. And then just keep checking his/her king on the empty board, until you get a fork/pin of his king and rook. Unless the pawns are in a special position, as in they are about to promote and you can't do anything about it, NEVER accept the draw.
61. Qc5 would also have finished the job much quicker, you get the fork after max 2 moves. And 53 Qd5+ would have spared even more trouble ...
These positions are rarely lost for the K + Q side, but they can be drawn in many cases. The most common involves a "fortress" where black's pawns are connected, ideally chained, with one of them defending his rook and his king is close enough to guard the more backwards pawn. In that situation white can check perpetually, but he can't gain a tempo or do anything to force the rook away from whatever rank/file it's controlling. With white's king unable to make the necessary inroads, mate is impossible.
Can't post the position because we didn't record the game as we played and I didn't think to copy the final position but I do remember it was a fortress position as described by pentiumjs. I was trying to fork him but this person is a very careful player and he wasn't going to allow it. His two pawns were chained together, one was a Rook's Pawn and the other was a Knight's Pawn and they were shielding his King and he wasn't moving those pawns and all I could do was check him back and forth but couldn't figure out a way to make him move his pawns or put his Rook and King in a forkable position. It was just a friendly game and he was getting impatient so I agreed to a draw. I would appreciate it if more readers can send in games along those lines with analysis.
I of course respect everyone's opinion, but would like to ask those making frank statements to NEVER ask for a draw how they'd achieve mate with the rook being guarded by the front pawn and reflexively guarding the rear pawn. The kings are on opposite sides of the board. Please tell me how the king (using the queen) can magically teleport to support his queen into a mate position? In this case our other king can wander around all day without a care in the world if there are no other pieces remaining. just saying folks.
I was playing a game in my chess club this afternoon and it came down to an endgame involving my King and Queen against my opponent's King, Rook and two pawns. I agreed to a draw. I didn't record the game or the position but did I do the right thing in agreeing to a draw?