Here the extra space arising from the fact that White has a c pawn instead of a b pawn creates enough space for White to advance the King and pawn without hindrance
1.Kb4
Rb8+
2.Ka5
Rc8
3.Kb5
Rb8+
4.Ka6
Rc8
5.Rc1
Ke7
6.Kb7
Rc5
7.Kb6
Rh5
8.c5
Kd8
9.Rd1+
Kc8
10.Rg1
Rh8
11.c6
Kb8
12.Rg7
Rf8
13.Rb7+
Kc8
14.Ra7
Kb8
15.c7+
Kc8
16.Ra8+
wins *