SOLUTION: At how many minutes after 5 PM will the hands of a clock become perpendicular for the first time?

Question 777842: At how many minutes after 5 PM will the hands of a clock become perpendicular for the first time?
Answer by Edwin McCravy(20055) (Show Source): You can 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

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