All rook endings are drawn-someone

Example 9-158 Dvoretsky’s Endgame Manual

White to Play(Diagram)

White has an extra pawn but Black’s rook is in an ideal defensive position, behind the passed pawn and targeting the f-pawn.

What does White do now? and what is the objective evaluation?

White to Play

Warning: You either know this or you don’t. This is very hard without prior knowledge.