SOLUTION: Between 12:00 and 1:00, when will the minute hand be 40 minute spaces ahead of the hour hand?

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Question 1011924: Between 12:00 and 1:00, when will the minute hand be 40 minute spaces ahead of the hour hand?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The hour hand will be somewhere between 12 and 1 on
the clock. It's speed is +5%2F1+ minute spaces/hr
-----------------------------
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%2F1+ 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 )
-------------------------------
+%28+60%2F1+%29%2At+-+%28+5%2F1+%29%2At+=+40+
+t%2A%28+60+-+5+%29+=+40+
+t+=+40%2F55+ hrs
Convert hrs to minutes
+t+=+%28+8%2F11+%29%2A60+
+t+=+480%2F11+
+t+=+43.6363+
and
+.6363%2A60+=+38.1818+
------------------------
The hands will be 40 minute spaces apart at
12:43:38