SOLUTION: Consider a correctly functioning clock that starts ticking at noon and find the time between noon and 1PM when the angle measure between the hands is 180 degrees.

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Question 630555: Consider a correctly functioning clock that starts ticking at noon and find the time between noon and 1PM when the angle measure between the hands is 180 degrees.
Answer by josmiceli(9697) About Me  (Show Source):
You can put this solution on YOUR website!
At exactly noon, the minute hand and the hour hand
are aligned.
For every 360 degrees the minute hand travels, the
hour hand travels +%285%2F60%29%2A360+=+30+ degrees
----------------
When the minute hand is somewhere between 6 and 7,
the hour hand is between 12 and 5.
Call the angle that the minute hand makes +a+
Call the angle the hour hand makes +b+
given:
+a+-+b+=+180+
The speed of the minute hand is 360 degrees/hr
The speed of the hour hand is 30 degrees/hr
-------------------------------------
If +t+ is the time in hours when the hands
are 180 degrees apart
+a+=+360t+
+b+=+30t+
so
+360t+-+30t+=+180+
+%28+360+-+30+%29%2At+=+180+
+330t+=+180+
+t+=+180%2F330+
+t+=+6%2F11+ hrs
+%286%2F11%29%2A60+=+32+%2B+8%2F11+
+%288%2F11%29%2A60+=+43+%2B+7%2F11+
The time will be 12:32 and 44 seconds approximately