A rook's superpower in the endgame isn't checking, it's fencing: parked on a file, it draws an uncrossable line down the board, and the enemy king simply cannot step over it. Cut the defending king off from your passed pawn and the pawn strolls to promotion while the king watches from behind the fence.
This idea decides more rook endgames than any tactic. The technique: place the rook on the file BETWEEN the enemy king and your pawn, as far from the king as possible so it can't be harassed. Every rank the king is cut off from is worth roughly a tempo in the race.
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White's c-pawn wants to run. The black king stands one file away from stopping it, unless a fence goes up.
Build the fence between the king and your pawn.
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