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A question in a current GCSE text runs thus: it is 1 o'clock on a standard Big Ben type clock face. At what time will the hour hand and minute hand next be in line?
Answer. Suppose this happens after n minutes; the hands will be in line just after 1. After 1 hour + 2n minutes the hands will be in line just after 2. … After 10 hours + 10n minutes the hands will be in line just after 10 (nearly 11 in fact). After 11 hours + 11n minutes it will be 12:00. So 11n = 60 mins, ie n=60/11.
(Or, more quickly, the hands will be in line 11 times in 12 hours. So the points at which this happens will form a regular 11-gon.)
Of course there is a 'straightforward' way of doing this involving degrees. In 1 minute, the minute hand moves 6° and the hour hand moves ½°.
