What is the first time (to the nearest second) after 12:00 midnight for which the minute hand and hour hand of a clock make a 30° angle?

Question

I need the answer expressed in minutes and seconds, please!

Answer 1

Between midnight and 1 AM, the hour hand moves 30°.

And the relationship between the degree location of the minute and the hour hand is h=m/12

Then the angle between the hands is m-m/12=11m/12.

11m/12=30 when m= 360/11.

When m=360/11, h=30/11

This is the solution: the angle of the minute hand is 360/11 and the hour hand is 30/11, i.e. the time is about 5 minutes and 27 sec after midnight.