SOLUTION: At 8 o'clock, the hour hand and the minute hand are perpendicular. They form straight line 16 4/11 minutes later. How many minutes after 9 o'clock are they perpendicular again?

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Question 321431: At 8 o'clock, the hour hand and the minute hand are perpendicular. They form
straight line 16 4/11 minutes later. How many minutes after 9 o'clock are they
perpendicular again?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
At 9 o'clock ... not 8

the hour hand moves 1/12 of a circle in 60 min ___ 1/2º per min

the minute hand moves 360º in 60 min ___ 6º per min

the starting angle is 90º ___ the hands will be perpendicular again when that angle is 270º

90 - (1/2)m + 6m = 270 ___ (11/2)m = 180 ___ m = 360/11 = 32 8/11 min


the wording of the problem shows that the angle increases 90º every 16 4/11 min
___ 2 * (16 4/11) = 32 8/11