Math CentralQuandaries & Queries


Question from Nazrul:

How many times in a day are the hands of a clock perpendicular to each other? How can I find the times? Please help me.

Hi Nazrul,

I can help you get started. Suppose we start at midnight when the two hands are pointed at 12. The minute hand revolves around the face of the clock at $360^o$ per hour and the hour hand revolves at $30^o$ per hour. At some time the hands form a right angle. Suppose this time is $x$ hours after midnight. At that time the minute has revolved $360 \times x$ degrees and the hour hand has revolved $30 \times x$ degrees. Since the hands are perpendicular we know that

\[360 x - 30 x = 90 \mbox{ which reduces to } x = \frac{3}{11} \mbox{ hours.}\]

Since there are 60 minutes in an hour we know that

\[x = \frac{3}{11} \times 60 = 16.36 \mbox{ minutes.}\]

When is the next time the two hands are perpendicular?


About Math Central
* Registered trade mark of Imperial Oil Limited. Used under license.


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina Imperial Oil Foundation