A Mile With the Wind, a Mile Against It — What's His True Pace?
A cyclist rides a mile with a tailwind in exactly 3 minutes, then turns around and pedals the same mile straight into that same wind, taking exactly 4 minutes. Most people's first instinct is to average 3 and 4 to guess his true no-wind mile time. Is 3.5 minutes actually correct?
Reveal the answer
No — averaging the times is the trap. The wind helped him for 3 minutes but hindered him for 4, so it's the rates (not the raw times) that must be combined: working from the actual speeds shows his true no-wind mile takes 3 minutes and 25 5/7 seconds (24/7 minutes), noticeably slower than the naive average of 3.5 minutes. From Sam Loyd's Cyclopedia of Puzzles (1914).
— Sam Loyd, Sam Loyd's Cyclopedia of Puzzles — Posthumous compilation edited by Sam Loyd Jr., 1914; puzzle "Riding Against the Wind"
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