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Suppose n=number of minutes elapsed. So the minute hand is pointing at n on the clock. Since n minutes elapsed, the hour hand should be pointing at
15+n/60*5
where 15 comes from the original position and n*5/60 is the time elapsed times the "speed" of the hour hand.
We assume that they pointed towards the same direction, so
n=15+n/12
and you will see that n=180/11.