A car goes out at 10 mph and back at 15 mph. What's the average speed for the round trip?
A motorist drives out to a town at an average of 10 miles an hour, then drives straight back along the exact same road at an average of 15 miles an hour. Most people's instinct is to just average the two speeds. What is the true average speed for the whole round trip?
Reveal the answer
12 miles an hour, not 12.5 as most people instantly guess. Over a 60-mile route each way, the outward leg takes 6 hours and the return takes 4 hours, so the full 120-mile round trip takes 10 hours — 120 ÷ 10 = 12 mph. You can't average two speeds by simply splitting the difference unless the time spent at each speed is equal. Henry Dudeney posed it as puzzle No. 67 in Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — 1917, Puzzle No. 67, 'Average Speed'
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