Answer to Puzzle #5: Degrees Between the Hands of a Clock

5. How many degrees (if any) are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

I worked this one out for myself too, this is one of the easier ones...

Before reading the answer can I interest you in a clue?

First consider the picture below:-

hands of a clock at 3.15

Clearly there is an angle between the hour and minute hand other than zero. This comes from the fact that the hour hand, having been exactly on the '3' at 3 o'clock, doesn't simply stay there whilst the minute hand is catching up. Rather it is one quarter of the way on it's journey to 4 o'clock. So let us consider the angles clockwise from 12 o'clock so.

12 o'clock = 0°
1 o'clock = 30°
2 o'clock = 60°
3 o'clock = 90°
6 o'clock = 180°

The simplest way to think of this is that each hour is made up of 30° and that the hour hand will have moved one quarter of an hour past three o'clock. ¼ x 30° = 7.5°

If you are interested in exactly what time the two hands overlap, when there zero degrees between them; I deal with this in Puzzle #35.

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