Answer to Question #237436 in Algebra for Mr. Lee

Question

In how many minutes after 2 o’clock will the hands of the

clock extend in opposite direction for the first time?

Answer 1

Analog clock has minimum of two hands to show time, one is an hours hand and the other is a minutes hand. There are 12 divisions of the hour in a clock and 60 divisions of minutes. When the minute hand goes through 60 divisions the hour hand goes through one division. 

The minute and hour hand are opposite of each other every hour except for one. So, in a full day this happens 22 times. 

We have to find time after 2'Oclock after which the hour hand and minute hand are exactly opposite. 

$30° (\frac{m}{60})+240°=360° (\frac{m}{60})\\0.5°m-6°m =-240°\\m = 43.63 mins$

Hence, the minute hand and hour are opposite to each other after 43.63 mins.