Rook vs. Pawn

The first rook ending in Thomas Engqvist, 300 Most Important Chess Positions (2018) is from a game that he won because his opponent did not know how to draw. I had an almost identical position in a blitz game twenty years ago with the same result.

White to move

57.Kb7??

57.Kd8 draws

57...Kd6 58.Ka7 Ra1+ 59.Kb8 Kc6 60.b7 Rb1 61.Kc8

61.Ka8 was worth a try, even though it leads to a faster checkmate. Maybe my opponent was hoping I could not checkmate with the rook in the time remaining.

61...Rxb7

Further exploration of my database revealed another instructive rook ending that should have been drawn. After my opponent's blunder, my play was near perfect.

White to move

47.e5??

47.Ke5=;
47.Kf5 a2 48.Ra7+ Ke8 49.Ke6 Kd8 50.Ra8+ Kc7 51.e5=

47...a2 48.Ra7+ Ke6 49.Ra6+

Black to move

49...Ke7

49...Kd7 is slightly better.

50.Ra7+ Kd8 51.Ra8+ Kc7 52.Ra7+ Kb6 53.Ra3

Black to move

53...Rf1+ 54.Kg5 a1Q 55.Rxa1 Rxa1 56.e6 Re1

56...Kc5 also wins

57.e7

57.Kf6 Kc5 still wins 58.e7 Kd6

57...Rxe7 White resigns 0-1

The second rook ending in Engqvist's book is a gem from Richard Reti.

White to move

Can you win with White?