Day Clock
Day Clock
How many times in a day do both hands of the clock point in the same direction and what are the times ? ?
I have to find out how many times a day do both clock hand point at the same direction and what times they are when they point at the same direction ?
24 times is incorrect. The correct answer is, the hour and minute hand meet 22 times.
The reason is, the hour hand also makes 2 revolutions around the clock each 24 hours. So you have to subtract these two from the 24 times that the minute hand spins around.
The minute hand has to travel a little further each hour to "catch" the hour hand, about an extra 5 minutes or so.
Starting at 12 midnight, they meet at: (approximately)
12 am
1:05 am
2:10 am
3:16 am
4:22 am
5:27 am
6:33 am
7:38 am
8:43 am
9:48 am
10:54 am (next meeting will be at 12 noon, not 11:55)
That's 11 times between midnight and noon. Change am to pm for the 11 times between noon and midnight. And midnight means the start of the next day, so we don't count that again.
2 x 11 = 22 times in 24 hours.
You can confirm this by taking any clock that you can set the hands on, like a wall clock or alarm clock - start the hands at 12 am, and spin the hands manually, counting all the times that the hands meet. You'll see that the minute hand has to travel a little further than an hour each time around in order to catch the hour hand.
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