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October 11th, 2018, 08:42 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  how to solve this confusing clock problem?
Q) At what time between 45, both hands of clock right angle side. A) The minute hand moves 1/60th of the way around every minute. So it moves 6° per minute. The hour hand moves 1/12th = 30° every hour. So it moves 0.5° every minute. At 4 o'clock, taking the 12position to be 0°, the minute hand will be at 0° and the hour hand will be at the 4position = 120°. After n minutes, the minute hand will be at (0+6n)° = (6n)° and the hour hand will be at (120+0.5n)°. We want the difference to be 90°, so; 120 + 0.5n  6n = 90 30 = 5.5n n = 5.454545 So the time will be 4:05:27 My friend got two answers: 4h60/11 min and 4h420/11 min. I am confused. 
October 12th, 2018, 12:46 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2222 
30/5.5 = 60/11 Your friend also found the time when the minute hand is 90° beyond the hour hand. 
October 12th, 2018, 03:33 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  
October 12th, 2018, 08:20 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2222 
As the minute hand is moving much faster than the hour hand, it will overtake it and reach an angle of 90 degrees with it before 5 o’clock.

October 17th, 2018, 11:23 PM  #5 
Member Joined: Sep 2017 From: Saudi Arabia Posts: 37 Thanks: 1  

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