Question Video: Telling How Many Times a Specific Hour Comes in the Day Mathematics

How many times a day does the clock show the given time?

02:23

Video Transcript

How many times a day does the clock show the given time?

The clock that the question’s talking about is shown in the picture. We know that at an o’clock time, the minute hand points to the number 12, but in this picture it’s pointing to the number three. It’s moved a quarter of the way around the clock face. This is a quarter past time. And if we look at the hour hand, we can see what hour of the day it is. The hour hand is on its way from the number six to the number seven. We know that at 6 o’clock, it would’ve been pointing exactly to the number six. And so, we can read this time as quarter past 6.

Now, our question asks us, “how many times a day does the clock show this time?” Now, it’s easy to make a mistake here. We might look at the time and just say, “Well, there’s only one-quarter past 6 every day.” But let’s use some facts to help us. Firstly, we know that 24 hours are the same as one day. When we say a day, we don’t just mean the daytime when the sun is up; we mean a whole day, for example, Monday or Tuesday. So this includes the daytime and the nighttime.

Another fact we can use to help us here is that the hour hand goes round the clock face once every 12 hours. It doesn’t matter what time of day it is. It takes 12 hours for it to go all the way around back to where it was. So if we look at our clock face and we think that our hour hand is in the exact position for quarter past 6, if 12 hours go by, it’s going to show quarter past 6 again. But there aren’t 12 hours in a day. There are 24 hours in a day. This is where we can use a number fact to help us. We know that 12 plus another 12 make 24.

And so, in a whole day, the hour hand doesn’t just go once around the clock; it goes twice. This clock is going to show the time quarter past 6 twice a day, quarter past 6 in the morning and then quarter past 6 in the evening. We know that the hour hand makes two journeys around the clock face in a day. And you know, it doesn’t really matter what time this clock shows. The number of times every day that a clock shows any time is always two.

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