SOLUTION: At what time after 12:00 noon will the hour hand and the minute hand of the clock first form an angle of 120 degree?

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Question 89634: At what time after 12:00 noon will the hour hand and the minute hand of the clock first form an angle of 120 degree?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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At what time after 12:00 noon will the hour hand and the minute hand of the clock first form an angle of 120 degree?
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Let x = position of the minute hand (in minutes) when this occurs
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The minute hand travels 360 degrees in 1 hr
The hr hand travels 360/12 = 30 degrees, in 1 hr
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The fraction of an hr can be expressed by x/60
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Min hand degrees - hr hand degrees = 120
%28x%2F60%29360 - %28x%2F60%2930 = 120
:
6x - .5x = 120
5.5x = 120
x = 120/5.5
x = 21.82 minutes or 21 min 49 sec
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