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.