SOLUTION: It is four o'clock now. How many minutes will pass before the minute hand and hour hand of the clock are pointing to the exact same place? (Hint: it is not 20 minutes, because by t

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Question 717922: It is four o'clock now. How many minutes will pass before the minute hand and hour hand of the clock are pointing to the exact same place? (Hint: it is not 20 minutes, because by the time the minute hand points to the 4, the hour hand will have crept ahead a little.)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
There are 60 minute-marks around the face of a clock.

The speed of the minute hand is 60 minute-marks per 1 hour,

or %2860_minute_marks%29%2Fhr or 60minute_marks%2Fhr

The speed of the hour hand is 60 minute-marks per 12 hours.

or %2860_minute_marks%29%2F%2812_hours%29 or 60%2F12minute_graduations%2Fhr or 5minute_graduations%2Fhr

At 4:00 the hour hand has a 20 minute-mark head start on the hour
hand, so the minute hand's catch-up rate is 60-5 or 55minute_marks%2Fhr.  
Since time = distance%2Frate, the minute hand will catch up to the hour hand
in 20%2F55 hr which reduces to 4%2F11 of an hour which is expr%284%2F11%29%2A60 minutes
or 240%2F11 minutes, or 21%269%2F11 minutes

That's  21 minutes and 49%261%2F11 seconds. 

Edwin