Expert: Scott A Wilson - 10/17/2009

Question
At what time between 3 to 4 o'clock will be the hands of the clock be together.

Please help me to find the answers of this problem, I really need it so badly. Thank you so much.

Answer
The hands on a clock depend on the time.

There are (360/12)° per hour, so 30° per hour.
There are 60 minutes in an hour, which is 30°, so this makes for 0.5° per minute.

That means the hour hand is at 90° + 0.5x°, since it is after 3 and x minutes have passed.

The minute hand moves 6° for each minute, so it is at 6x.

To find where thow two are on top of each other, set 6x = 90 + 0.5x.

Subtract off the 0.5x from both sides and get 5.5x=90.

Divide both sides by 5.5 and get x = 90/5.5 = 180/11 = 16 4/11.

This means that at 16 4/11 minutes past the hour during the 3 o'clock hour,
the hour and minute hand are on top of each other.