Question 630555
At exactly noon, the minute hand and the hour hand 
are aligned.
For every 360 degrees the minute hand travels, the
hour hand travels {{{ (5/60)*360 = 30 }}} degrees
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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
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If {{{ t }}} is the time in hours when the hands
are 180 degrees apart
{{{ a = 360t }}}
{{{ b = 30t }}}
so
{{{ 360t - 30t = 180 }}}
{{{ ( 360 - 30 )*t = 180 }}}
{{{ 330t = 180 }}}
{{{ t = 180/330 }}}
{{{ t = 6/11 }}} hrs
{{{ (6/11)*60 = 32 + 8/11 }}}
{{{ (8/11)*60 = 43 + 7/11 }}}
The time will be 12:32 and 44 seconds approximately