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put this solution on YOUR website! At how many minutes after 5 PM will the hands of a clock become perpendicular for the first time?
The angular speed of the minute hand is 360° per hour or 6° per minute.
The angular speed of the hour hand is 360° per 12 hours or 30° per hour,
or 1/2 a degree or 0.5° per minute.
The catch-up rate of the minute hand to the hour hand in the vicinity
of 5 PM is the difference in their angular speeds or 6°-0.5° or 5.5°
per minute.
That is, in the vicinity of 5 PM the angle between the two hands is
shrinking at the rate of 5.5° per minute.
At 5 PM the hour hand is 5/12ths of 360° or 150° ahead of the minute hand.
We want to find when the hour hand will have shrunk from 150° down to
90°, which is a decrease of 60°.
Answer: time = angle/rate = 60°/5.5° = 600/55 = 120/11 = 10 10/11 minutes.
Edwin
