Carroll's Tangled Tale: Two Travelers and a Hill
In Lewis Carroll's 'A Tangled Tale,' two travelers leave at 3 o'clock and get home at 9, walking a level road, up a hill, and down again. On the level they walk 4 miles an hour, uphill 3, downhill 6. How far did they walk in all — and can you pin down, to within half an hour, when they reached the top of the hill?
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They walked 24 miles. A there-and-back mile always takes exactly half an hour, whether level (1/4 hour each way) or hill (1/3 hour up, 1/6 hour down) — so six hours of walking means twelve miles out and twelve back. But because the road could split between level and hill stretches in different ways, Carroll himself could only pin the summit time down to within half an hour of 6:30. From Lewis Carroll's 'A Tangled Tale,' Knot I: 'Excelsior' (1880).
— Lewis Carroll, A Tangled Tale — Knot I, "Excelsior" (serialized in The Monthly Packet, 1880)
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