SOLUTION: Determine the smaller angle between the hands of a clock at 12:20. Show or explain how you got your answer.

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Question 603010: Determine the smaller angle between the hands of a clock at 12:20. Show or explain how you got your answer.
Found 2 solutions by solver91311, AnlytcPhil:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The angular difference between the 12 where the minute hand was at exactly 12 and the 4 which is where the minute hand is at exactly 12:20 is exactly one-third of a circle. But while the minute hand was moving through this one-third of the whole circle, the hour hand was moving one-third of the way from the 12 (where it was at 12 o'clock exactly) to the 1 (where it will be when the minute hand gets all the way back around to the 12). The angular difference between the 12 and the 1 is one-twelfth of a circle. So the minute hand has moved a full one-third of the circle but the hour hand has moved one-third of one-twelfth of the circle. Then recall that there are 360 degrees in a circle.



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Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Determine the smaller angle between the hands of a clock at 12:20. Show or explain how you got your answer.
Here's another approach which amounts to the same thing as the other
tutor's explanation, but may be easier for some people to inderstand:

The hour hand makes 360° in 12 hours, so
the angle speed of the hour hand is 360/12 or 30 degrees/hour.

The minute hand makes 360° in 1 hour, so
the angle speed of the minute hand is 360 degrees/hour. 

The hands were together at 12:00.  12:20 is 20 min. or 1/3 hr.
later.  So in that 20 minutes or 1/3 hr., 

the hour hand has swept through (1/3 hr)×(30degrees/hr) or 10 degrees,

and

the minute hand has swept through (1/3 hr)×(360degrees/hr) or 120 degrees.

Therefore the angle between them at 12:20 is 120°-10° or 110°
 
Edwin
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