at what time from 8 to 9 the hands of the clock are in opposite direction
Answers
Given : A clock time between 8 & 9
To Find : at what time from 8 to 9 the hands of the clock are in opposite direction
Solution:
At 8 o clock
Hour hand is at ( 8/12) * 360 = 240°
Minute Hand is at 0°
Now hands of the clock to be in opposite direction
Angle between them = 180°
If Hour Hand moves x° Then Minute hand should move (60 + x)°
Minute hand moved 360° in 60 minutes
=> 6° in 1 Minute
Hour Hand moves 360° in 12 Hr
Hour Hand moves 30° in 1 Hr
Hence 0.5° in 1 minute
Hour hand moves 1° in 2 Minutes
=> Hour hand moves x° in 2x minutes
Minute hand moved in 2x minutes = 6 * 2x = 12x°
12x° = (60 + x)°
=> 11x = 60
=> x = 60/11
2x = 120/11 minutes = 10.91 minutes ≈ 11 minutes
At 8 hr 11 Minutes hands of the clock are in opposite direction
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