Late Again

kendall/thomas railroad puzzle

A problem from P.M.H. Kendall and G.M. Thomas’ Mathematical Puzzles for the Connoisseur, 1962: A road runs parallel to a railway until it bends to cross it, as shown. A man normally cycles to work along the road at a constant speed of 12 mph, and when he reaches the crossing he’s normally overtaken by a train traveling in the same direction. One day he was 25 minutes late for work and found that the train passed him 6 miles before the crossing. What was the speed of the train?

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