Question

IB exams

At what time between 6 and 7 will the hands be perpendicular?

Answer 1

let us say  X minutes past 6 o clock, the hands are perpendicular.  X < 60 .

hours hand moves 360 deg. in 12 hours.
    =>  30 deg in 1 hour. => 1/2 deg in 1 minute
minutes hand  moves 360 deg  in 1 hour 
         => 6 deg. in 1 minute

the angle moved by hours hand in X minutes = X/2 deg.
the angle moved by minutes hand in X minutes = 6 X deg.

The difference must be  90 deg.  or  270 deg.
 
    6 X - X/2 = 90 deg.    => 11/2  X  = 90      =>  X = 180/11 = 16.36 min
                    
   6 X - X/2 = 270 deg    =>   X = 540/11 = 49.09 min

So  at  6 hrs 16.36 min  and  at  6 hours  49.09 min,  the hands are perpendicular.