This particular Rook Endgame taught me 101 lessons. It's all been building up from working progressively through Chess Informant's Encyclopaedia of Chess Endings II (Rook Endings). Piece by piece I'm being introduced to 3 file checking distance, breaking blockades and shouldering.
Here it is Black to Move, from Position 174
Black to Move
The key idea here is to make the e4 advance as difficult as possible.
White will attempt to play Rg4 and settle his Rook there. After this, he can advance e4.
Given any Rook move either allows e4, or takes away one of the ranks closer to the pawn, then logically only 1. ... Kh6 remains.
Don't let the Rook settle
Break the Shoulder: What Not To Do
This is what not to do. The check does nothing but allow White's King to access e7 with tempo. As the Black Rook must move, White gains e4 with tempo.
This takes one of the 3 ranks away for the checking distance. Checks along the ranks are futile, as White's King can use his pawn as a shield once he steps on the f-file.
Break the Shoulder: What to Do
Instructive for me was the whole purpose of the check at f8 to make the White King give up control of g5.
Even if the White King went to g7, then after dancing with Re8, Kf7 Ra8 (to be 3 files away), the Black King accesses g5 to not allow shelter from horizontal checks.
Which square to go to?
Blockading with Ke7
e7 was a bad choice because after Rf7+ and Kd6, the Black King is imprisoned with a check at a8 inevitable.
We see that Kg6 is bad, as Black must concede Kg7 anyway, and White's King makes progress to f6 which decides matters as Black falls into zugzwang.
By saving a move, Black is able to retreat his Rook to a8 to prepare the horizontal checks while his King can hide at f8 where it is not impeded by his own Rook.