pawn endgame


Why is the Black King moving up the f-file after 1.Kh2 Kf2 2.Kh3 Kf3? Black wins by just marching over to the white pawn as fast as possible.

Why is the Black King moving up the f-file after 1.Kh2 Kf2 2.Kh3 Kf3? Black wins by just marching over to the white pawn as fast as possible.
...and the White King gets to the Black pawn and game drawn.