You can put this solution on YOUR website! When will the two hands of a clock between 10 O'clock and 11 O'clock come in the same line?
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Let m = position of the min had based on a 60 min circle
The hr hand will be between the 50 and 55th min also, determined by the fraction m/60 times 5 minutes.
m = 5 + 50
m = + 50
mult equation by 12 to get rid of the fraction
12m = m + 600
11m = 600
m = 600/11
m = 54.545 min which is 54 + .545(60) = 54 min 38 seconds
At 10:54:38 sec the hands will be in line
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Well that is different, see if we can find that.
There will be exactly 30 min between the hands
m + 30 = 5 + 50
subtract 30 from both sides
m = + 20
mult equation by 12 to get rid of the fraction
12m = m + 240
11m = 240
m = 240/11
m = 21.82 min which is 21 + .82(60) = 21 min 49 seconds
At 10:21:49 sec the hands will be in line
