# Clock and problem

1. Jun 6, 2013

a clock was set 10 am 20 minutes 30 second ? what will be the angle between hour & second hand ??

ans : 130.25° or 133° which one is correct? I'm confused

2. Jun 6, 2013

### Ryuzaki

The line of reasoning should be as follows:-

It takes 12 hours for the hour hand to make a complete 360° rotation, i.e.

12 hours-------> 360°
==> 1 hour -------> 30°
==> 60 min -------> 30°
==> 1 min -------> 0.5°
==> 20.5 min -------> 10.25°

So, in a time period of 20.5 minutes, the hour hand would have traversed 10.25°.

Now, when the clock shows 10 A.M exactly, the hour hand has traversed 300° (since for each hour, the hour hand traverses 30°. So, after 10 hours exactly, it has traversed 300°). And in a further 20 minutes and 30 seconds, i.e. 20.5 minutes, it would have traversed 10.25° further, as we have just calculated above. So, the total angular distance traversed by the hour hand is (300+10.25)° = 310.25°.

Now, the second hand is at the exact position '6' in the clock (since it travels for a period of 30 seconds), and hence has traversed exactly half of the clock, thus travelling an angular distance of 180°.

Therefore, the angle between the hour hand and the second hand would be (310.25 - 180)° = 130.25°.

Hope that makes it clear!

3. Jun 6, 2013

### jbriggs444

The more interesting question is how the other answer was obtained.

Offhand, it looks like a factor of 12 got erroneously applied to the seconds correction.

4. Jun 6, 2013

### Ryuzaki

The best explanation I could come up with is, that the OP first figured that at exactly 10:20 A.M, the hour hand would have traversed 310°. Then, for the remaining 30 seconds, he mistakenly calculated the angular distance traversed by the minute hand, which turns out to be 3°, and then added it to the angular distance traversed by the hour hand, giving him the final value of the latter as 313°. And since the second hand has traversed 180°, he obtains (313 - 180)° = 133°, which is false.

5. Jun 6, 2013

### jbriggs444

Nice. That fits.

6. Jun 11, 2013