1.Rf4
The rook needs to be on the 4th rank in order to provide shelter for the king, which is going to wind up on g5.
1...Rh1
Black stays on the h-file in order to keep thw White king as restricted as possible. [ If instead 1...Rg2
then White's rook takes over the h-file, allowing his king into h8. - Keres 2.Rh4
Kf6
3.Rh6+
Ke7
4.Kh8
Kf7
5.Rh7
]
2.Re4+
Creating space for his king by moving the Black king back a file. [ White gets nowhere by 2.Rf7+
Ke8
3.Rf8+
Ke7
as his own king is still trapped.]
2...Kd7
It makes no difference where the Black king goes: d6 and d8 all have the same result.
3.Kf7
At last the king gets out from in front of his pawn.
3...Rf1+
All Black can do is try to keep checking the White king and hopefully drive him back in front of his pawn again.
4.Kg6
Rg1+
5.Kf6
Rf1+
6.Kg5
Now you can see why the White rook was needed on the 4th rank - after the coming check White can interpose the rook.
6...Rg1+
7.Rg4
The pawn can not be stopped. *