Question 1011924
The hour hand will be somewhere between 12 and 1 on
the clock. It's speed is {{{ 5/1 }}} minute spaces/hr
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The minute hand will go a little beyond the 40 minute
since the hour hand is moving at the same time.
It's speed is {{{ 60/1 }}} minute spaces/hr
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In words:
[ rate of minute hand ]x[ time elapsed ] minus [ rate of hour hand ]x[ time elapsed ]
equals [ 40 minute spaces ]
( note that time is in hours )
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{{{ ( 60/1 )*t - ( 5/1 )*t = 40 }}}
{{{ t*( 60 - 5 ) = 40 }}}
{{{ t = 40/55 }}} hrs
Convert hrs to minutes
{{{ t = ( 8/11 )*60 }}}
{{{ t = 480/11 }}}
{{{ t = 43.6363 }}}
and
{{{ .6363*60 = 38.1818 }}}
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The hands will be 40 minute spaces apart at
12:43:38