A Walking Puzzle

A man set out at noon to walk from Appleminster to Boneyham, and a friend of his started at two P.M. on the same day to walk from Boneyham to Appleminster. They met on the road at five minutes past four o'clock, and each man reached his destination at exactly the same time. Can you say at what time they both arrived? Source: Henry Ernest Dudeny, 536 PUZZLES & Curious Problems, Scribner's, 1967, #59.
[Taken from Ken's Puzzle of the Day, October 12, 1994.]

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