For an ACCURATE clock the minute hand travels TWELVE times faster than the hour hand.
the minute hand travels at 6 degrees/min and the hour hand at 1/2 degrees/min (d/m)
For the two hands to meet then
6 d/m * x -360 = 1/2 d/m * x where 'x' is in minutes
solve for x
x = 65.454545 minutes or 65 min 27.27 seconds
If the faulty clock's hands meet at 65 minutes exactly it has gotten to that point 27.27 seconds EARLY and is running FAST.
It gains 27.27 seconds in 65 minutes or
27.27/65 = t/60 where t = time gained per REAL hour
The faulty clock GAINS t = 25 seconds each REAL hour.
