## PRIZE PUZZLE FOR DECEMBER 2004

Fred Everready visits his mother every Sunday, by car. For the first quarter of his journey he drives at an average speed of 40 miles per hour. His average then increases to 60 mph for half the total distance, which is mainly on motorways, but his average falls back to 40 mph for the final quarter of the way. What is Fred's average speed over the whole journey?

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 The average speed is 48 miles per hour, not 50. The average speed would be 50 if the journey were divided into halves by time, but it is not: it is divided into halves by distance and the correct value is the harmonic mean, not the arithmetic mean. The harmonic mean is the reciprocal of the mean reciprocal. Three members submitted the right answer: Gordon Stonham, Peter Greenhalgh and John Stafford, but John Stafford was excluded from the draw because he was the winner last month. That left only two and the draw only takes place for three or more persons. So no one wins this month and the prize will be added to the next month's prize puzzle draw; that is, for January 2005.