45. At what time between 6 and 7 will the hands be perpendicular?
Answer:
At 6 the angle between the hands is 180 deg.
To form 90 deg they have to cover 90 deg (out of 180 if 90 is covered 90 will remain)
So no. of minutes required = 90 / 5.5 = 180 / 11 = 16 4/11 min.
But they will be perpendicular for two times. The second one will happen after the minutes hand crosses the hours hand and then for 90 deg.
So it has to travel 180+90 = 270 deg.
So time = 270 / 5.5 = 540 / 11 = 49 1/11 min.
