There are two times between 5 AM and 6 AM when the hands of an accurate clock are perpendicular. Exactly how many minutes elapse between these two times?
My understanding is that by "perpendicular" you mean when they are 90 degrees apart. If so, then:
90=abs((30*5) - (5.5*M)), solve for M
M =10.909090....minutes after 5 AM when the 2 hands are 90 degrees apart.
270=abs((30*5) - (5.5*M)), solve for M
M =43.636363.....minutes after 5 AM when the 2 hands are 90 degrees apart, the 2nd time.
So, the time elapsed between the two periods equals:
43.636363.... - 10.909090..... =32.727272......minutes elapsed between the 2 periods.