On new Year’s Eve every eyes will certainly be on the clock! even if it is in new York City, Tokyo or London – civilization all end the people will be watching the minute hand as it ticks closer come midnight. During this time, we gather roughly the beautiful clocks and the towers that organize them. Take it a look in ~ some renowned clock towers shown here. Deserve to you name all of them or simply some? execute you recognize why they are famous?


Watch exactly how the hands move approximately the face of the clock. They sometimes come together, then they move apart and also create a range of angles. I think the your head is now complete of fascinating questions around the sample of this motion. And, that course, you desire to answer every one of these questions. In ~ first, they could seem difficult, puzzling, and outright weird!

Wait a moment and think around it carefully. The hands move along the confront of the clock simply the

same method as tiny horses run about a circus ring. In one hour, the minute hand turns a complete circle (that is, 360o). This means that the hand moves with the speed of 360o every hour. The hour hand moves lot slower than that. In one hour, it just covers a 30o edge (this is the angle in between the two surrounding numbers the represent hours on the clock face). Therefore, the speed of the hour hand is 30o every hour. We have the right to do just about anything currently that we understand how fast our ‘horses’ space running.

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While we were liven thinking, the brand-new Year arrived! Both the hour and also the minute hands allude to 12, and also we deserve to hardly tell castle apart. Eventually, the minute hand will certainly overtake the hour hand. As soon as will they fulfill again? following year perhaps? I’m simply kidding, of food – they will come together lot sooner 보다 that!

Problem 1.


The brand-new Year is upon us and also the clock has struck 12. How many times will certainly the minute and the hour hands meet in the following 12 hours? once will it is in the following time they meet? (Both noon and also midnight have to be included.)

new Year’s night is a wonder time. Imagine a little elf living inside a clock. That fixes, cleans and winds it up every night. This specific elf was obtaining bored as he waited for the arrival of the brand-new Year, and he made decision to walk for a Ride!

Problem 2.


The tiny elf boarded the minute hand at noon and started riding on the hand of the clock every the while complying with just one straightforward rule. Every time that the minute and also the hour hand met, the elf hopped from one hand to the other. How numerous revolutions about the clock challenge will the elf make prior to midnight?

Problem 3.

On new Year’s eve night, the elf chose to finish a lot more an overwhelming stunt. The hopped onto

the seconds hand and also started talk while complying with the same dominion as before (but this time it also included the secs hand). Follow to the rule, if a clock hand v the elf on the meets among the various other two, then the elf switches over. How numerous revolutions will certainly the elf make in one hour?

Problem 4.

How plenty of times, in 24 hours, do the minute and hour hands type a right angle?

Tip. At an initial this shows up to be an entirely brand-new problem but, interestingly, you can use the solution to trouble 1.

The problem listed below is a variation on problem 3, and is a breeze if you’ve currently tackled the one.

Problem 5.

How countless times, in a 24-hour period, do the hour and also minute hands confront in opposite direction while in ~ the very same time gift positioned in a straight line.

Finally, below is a bonus problem for the experts. Rather of giving out the answer, us ask that you send it to usat info

Problem 6.

A stopwatch mirrors that the hour and also the minute hands both relocate at a constant, however inaccurate, speed. The 2 hands come throughout each other every 66 minutes. Is this clock too fast or two slow?

Don’t stop here! Think of new problems and send them to us at info
chathamtownfc.net.com. We deserve to solve them together!

Answers and also solutions:

Problem 1

Solution. The hour hand will certainly go roughly one time, and the minute hand will certainly go around 12 times. Together it renders one complete turn roughly the clock face, the minute hand meets the hour hand exactly one time.At the an initial revolution, the 2 hands meet beforehand on. In ~ the last revolution, lock will accomplish at the finish of your journey. ~ the hand meet, the angle between them starts to increase due to the fact that the minute hand moves quicker than the hour hand. The hand will accomplish again once the angle between them will 360o. In one hour, the minute hand consists 330o an ext than the hour hand. Therefore, the angle between the hands rises at the rate of 330o per hour. They fulfill after 360: 330/hr = 12/11 hrs or 1 hour 5 5 /11 minutes.

Answer: after ~ 1 hour and also 5 5/11 , 12 times.

Problem 2

Solution. The minute hand will certainly go 12 ring in this span of time. Because that the first round, the gnome will ride all the means on the minute hand. As the minute hand moves right into the 2nd round, the gnome will certainly hop top top the hour hand and also rest a while due to the fact that the hour hand moves slowly. While doing the third round, the minute hand will take the gnome come the 12 o’clock point. And so, it continues. As soon as the minute hand provides its fourth round, the gnome will hop over to the hour hand. During the 5th round, the gets earlier onto the minute hand and rides on it to the end of the round etc. In summary, the minute hand will take the elf come the finish of a round at 1pm, 3pm, 5pm, 7pm, 9pm and also 11pm. In ~ 12pm , that will record a ride on the hour hand to the end of that round.

Answer. 7 revolutions.

See more: How Did The Peace Of Westphalia Lay The Foundations Of Modern Europe ?

Problem 3

Answer. 21 revolutions.

Problem 4

Solution. Native midnight come midnight, the hands will satisfy each other 23 times (see trouble 1) v 22 intervals in between these encounters. In between every 2 encounters, the angle formed by the clock hands progressively increases from 0o come 360o. Within every of these intervals, there will certainly be two instances as soon as the hands are positioned perpendicular to each other – the angles space 90o and 270o. There are 22 intervals altogether. Therefore, the hands form a appropriate angle 2 x 22 = 44 times in 24 hours.