Question

At what time after 4 o clock, is the minute hand exactly aligned with the hour hand?

Answer 1

☆☆ranshsangwan☆☆


Assume that X minutes after 4.00 PM minute hand exactly
aligns with and hour hand. 

For every minute, minute hand travels 6 degrees. 

Hence, for X minutes it will travel 6 * X degrees. 

For every minute, hour hand travels 1/2 degrees. 

Hence, for X minutes it will travel X/2 degrees. 

At 4.00 PM, the angle between minute hand and hour hand is
120 degrees. Also, after X minutes, minute hand and hour
hand are exactly aligned. So the angle with respect to 12
i.e. Vertical Plane will be same. Therefore, 

6 * X = 120 + X/2 

12 * X = 240 + X 

11 * X = 240 

X = 21.8182 

X = 21 minutes 49.5 seconds 

Hence, at 4:21:49.5 minute hand is exactly aligned with the
hour hand.