Is it possible to draw this endgame where I blundered my queening pawn? Move 13 (54 in actual game) is when I blundered my last pawn due to pressure of the Blitz game (probably). Even with seemingly equal material, the position is dreaded as the Black's pawns are more than pawns, and the only possible way to prevent defeat is to find a perpetual or keep checking for fifty moves. Is that possible in this position?

(The replayer PGN is only excerpt. If you're interested to see the full action of how I lost in the KQ v KR ending, the game was played here.)

[FEN "8/5ppp/4p3/2k1P2P/2pp1nP1/8/3K4/2R5 w - - 0 42"]
[Date "2015.07.23"]
[White "Unihedron"]
[Black "Xyuzhg"]
[Result "0-1"]
[Variant "Standard"]
[TimeControl "300+3"]

1. Rf1 c3+ 2. Kc2 Ng2 3. Rxf7 Ne3+ 4. Kc1 Nxg4 5. Rxg7 Nxe5 6. Rxh7 d3 7. Rc7+ Kd4 8. h6 Ng6 9. Rc6 c2 10. Rxe6 Ne5 11. h7 Kc3 12. Rd6 Nf7 13. h8=Q+ Nxh8 14. Rd8 Ng6 15. Rd6 Nf4 16. Rc6+ Kb3 17. Rc8 Ne6 18. Rc6 Nd4 19. Rc7 Kb4 20. Rd7 Kc3 21. Rc7+ Kb4 22. Rd7 Kc5 23. Rc7+ Kd6 24. Rc8 Ke5 25. Re8+ Kf4 26. Rf8+ Ke3 27. Re8+ Kf2 28. Rf8+ Nf3 29. Rd8 Ne5 30. Rf8+ Ke2 31. Rd8 Nc4 32. Re8+ Ne3 33. Rd8 Nf5 34. Re8+ Kf3 35. Re5 Nd4 36. Rd5 Ke3 37. Re5+ Kf4 38. Rd5 Ke4 39. Rd8 Ke3 40. Re8+ Kf4 41. Rf8+ Ke5 42. Rd8 Nb3+ 43. Kb2 c1=Q+
There is a third way to draw this endgame - sacrifice your rook for two pawns. With only a knight, Black will not be able to checkmate you.

So from move 14 on, you should keep checking the king, or, if the king doesn't protect c2, attack c2. Black will never be able to escape.

A possible sequences of moves:

[FEN "7n/8/3R4/8/8/2kp4/2p5/2K5 w - - 0 42"]

1. Rc6+ Kb3 2. Rb6+ Ka4 3. Rc6 Kb3 4. Rb6+ Kc4 5. Rc6+ Kd5 6. Rxc2 dxc2 7. Kxc2 draw