SOLUTION: At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle?

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Question 102944: At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle?
Answer by scott8148(6628) About Me  (Show Source):
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the straight angle occurs when the angle between 12 and the minute hand equals the angle between 6 and the hour hand

the space between clock numbers is 360°/12 or 30°

the speed of the minute hand is 360°/60min or 6°/min
the speed of the hour hand is 30°/60min or .5°/min

let x=minutes after 7:00 ... 6x=30+.5x ... 5.5x=30 ... 55x=300 ...x=60/11

x=5 5/11 min ... 60(5/11)=300/11=27 3/11 sec

time is 7:05:27 3/11