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At what time between 7 and 8 on an analog clock do the hour and minute hand overlap?

  • Algebra -

    At 7:00 the hour hand has gone through 210° , and angle between the two hands is 210°

    the hour hand moves 30° per hour or 1/2 ° per minute
    while the minute hand moves 6 degrees per minute
    so the minute is gaining on the hour hand at the rate of 5 1/2 or 11/2 ° a minute
    So to make up the 210° would take 210÷(11/2)
    = 420/11 minutes or 38 2/11 minutes or 38 : 10.9 minutes

    so the time is 7 : 38 : 10.9

    The above becomes a general solution;
    at any time between t and t+1 o'clock,
    divide t by 11/2 to find the minutes past t o'clock when the hands overlap

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