After 3 Oclock When Do the Hours and Minutes Hand Meet Again
On New year's day's Eve all eyes will be on the clock! Whether in New York City, Tokyo or London – people all over the world volition be watching the minute hand equally it ticks closer to midnight. During this time, we gather around the cute clocks and the towers that hold them. Take a await at some well-known clock towers shown here. Can y'all name all of them or only some? Practise you lot know why they are famous? Lookout how the hands move around the face of the clock. They sometimes come together, then they movement apart and create a variety of angles. I think that your head is now total of fascinating questions about the pattern of this motility. And, of course, you want to answer all of these questions. At showtime, they might seem hard, puzzling, and outright weird! While we were busy thinking, the New year arrived! Both the hour and the minute easily indicate to 12, and we tin can hardly tell them apart. Somewhen, the minute hand will overtake the hr hand. When will they come across again? Next twelvemonth possibly? I'm just kidding, of course – they will come up together much sooner than that! Trouble 1. The New year's day is upon u.s. and the clock has struck 12. How many times will the minute and the 60 minutes hands meet in the adjacent 12 hours? When will be the side by side time they see? (Both apex and midnight should be included.) New year's day's Eve is a magical fourth dimension. Imagine a little elf [OF2] living inside a clock. He fixes, cleans and winds information technology up every nighttime. This particular elf was getting bored as he waited for the inflow of the New year, and he decided to Become for a Ride! Trouble 2. The piddling elf boarded the minute hand at noon and started riding on the hands of the clock all the while following just one simple rule. Every time that the minute and the hr hands met, the elf hopped from ane hand to the other. How many revolutions effectually the clock face up volition the elf make before midnight? Trouble three. On New year's day'south Eve night, the elf decided to complete a much more than difficult stunt. He hopped onto Problem 4. How many times, in 24 hours, do the infinitesimal and hour hands form a right bending? Tip. At first this appears to exist an entirely new trouble but, interestingly, y'all tin use the solution to problem ane. The problem below is a variation on problem three, and is a cakewalk if you lot've already tackled that one. Trouble five. How many times, in a 24-hr period, do the hour and minute easily face in opposite directions while at the same time existence positioned in a straight line. Finally, hither is a bonus problem for the experts. Instead of giving out the answer, nosotros ask that y'all ship it to usat info@russianschool.com. Problem 6. A stopwatch shows that the hr and the infinitesimal hands both move at a abiding, but inaccurate, speed. The ii hands come beyond each other every 66 minutes. Is this clock besides fast or two slow? Don't finish here! Think of new problems and send them to us at info@russianschool.com. We tin solve them together! Answers and solutions: Problem 1 Solution . The 60 minutes hand will go around in one case, and the minute mitt volition go around 12 times. As it makes 1 consummate turn around the clock face, the minute hand meets the hour hand exactly one fourth dimension.At the first revolution, the two easily meet early on. At the last revolution, they volition meet at the end of their journey. Subsequently the hands encounter, the angle between them starts to increase because the minute hand moves faster than the hour mitt. The hands will see again when the angle between them reaches 360 o . In an hour, the minute hand covers 330 o more than the hr hand. Therefore, the angle betwixt the hands increases at the rate of 330 o per hour. They meet later on 360: 330/hr = 12/11 hours or one 60 minutes five five /eleven minutes. Answer : after ane 60 minutes and 5 5/11 , 12 times. Trouble 2 Solution . The minute hand will go 12 rounds in this span of time. For the starting time round, the gnome volition ride all the way on the minute hand. Every bit the minute hand moves into the second round, the gnome will hop onto the hour mitt and rest a while since the 60 minutes manus moves slowly. While doing the tertiary round, the infinitesimal hand will take the gnome to the 12 o'clock point. And so, information technology continues. When the minute paw makes its fourth circular, the gnome will hop over to the hr hand. During the fifth round, he gets dorsum onto the minute hand and rides on it to the end of the circular etc. In summary, the infinitesimal manus will take the elf to the end of a round at 1pm, 3pm, 5pm, 7pm, 9pm and 11pm. At 12pm , he will catch a ride on the hour hand to the end of that round. Answer . vii revolutions. Trouble 3 Respond. 21 revolutions. Problem iv Solution. From midnight to midnight, the hands volition meet each other 23 times (meet problem ane) with 22 intervals between these encounters. Between every two encounters, the angle formed by the clock easily gradually increases from 0 o to 360 o . Inside each of these intervals, there will exist two instances when the hands are positioned perpendicular to each other – the angles are ninety o and 270 o . There are 22 intervals altogether. Therefore, the hands form a right angle ii x 22 = 44 times in 24 hours. Respond. 44 times. Problem v Answer. 22 times. 
Wait a moment and recollect about it carefully. The hands move along the face of the clock just the 
aforementioned way as piffling horses run around a circus ring. In one hr, the minute hand turns a total circle (that is, 360o). This ways that the hand moves with the speed of 360o per 60 minutes. The hour hand moves much slower than that. In one hour, information technology simply covers a 30o angle (this is the angle betwixt the two adjacent numbers that represent hours on the clock confront). Therefore, the speed of the hour hand is 30o per hour. We tin practice just nearly anything at present that we know how fast our 'horses' are running. 
the seconds hand and started riding while post-obit the same rule as before (but this fourth dimension it also included the seconds hand). According to the dominion, if a clock manus with the elf on it meets ane of the other ii, then the elf switches over. How many revolutions volition the elf make in ane hour?
Tags: math on the go, math games, holiday math
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