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April 1st, 2026 (Permalink)
From the E-Mailbag
A reader writes to ask:
If I ride my bicycle one mile at thirty miles per hour (MPH) to the top of a hill, how fast will I have to coast down the other side for a mile to average sixty MPH for the whole two-mile trip? A friend told me ninety MPH but I can't get the math to work. Help!
Can you solve the reader's problem?
What is the date of this entry?
It's impossible.
Explanation: To average sixty MPH, he would have to cover the two miles at an average of a mile a minute, which would take two minutes. However, it took him two minutes to climb to the top of the hill at thirty MPH. Therefore, he would have to cover the second mile instanteously, which is not possible even going downhill.
Disclaimer & Disclosure: This puzzle is fictional as is the e-mail. This is my version of a traditional "gotcha" puzzle often given in terms of a one-mile race track. I'd seen it before but was reminded of it by the following book: David J. Bodycombe, The Riddles of the Sphinx (2007), pp. 276 & 536.