Cuckoo Clock
At this moment the conversation was interrupted by a loud "Cuckoo" Dr. Chronos had just entered with a large cuckoo clock under his arm.
"Your clock is not exactly right," said Stars.
"Well It's not exactly wrong either," said Chronos, sitting next to Mr. Striker, who was puffing away on a cigarette. "You see, this is a very special clock: the hands shows the right time, but the cuckoo only emerges when the hands on the clock coincides."
If the bird was on time and the time was roughly 2:00 PM, what time was it exactly ?
"Your clock is not exactly right," said Stars.
"Well It's not exactly wrong either," said Chronos, sitting next to Mr. Striker, who was puffing away on a cigarette. "You see, this is a very special clock: the hands shows the right time, but the cuckoo only emerges when the hands on the clock coincides."
If the bird was on time and the time was roughly 2:00 PM, what time was it exactly ?
Labels: mathemagic, thinktank
posted by Rajesh Lal at
2:41 AM
11 Comments:
Its time to send the bird to rehab for excessive drinking on the job as after lunch he keeps getting later and later, plus is seriously hungover in the morning :)
2:11.55
At 2:12, the big hand is at the 12 and the small hand would be pointing exactly one minute's worth past the 2, or 1/5 of the way between 2 and 3 (12 minutes is 1/5 of the way through the hour). So the big hand would be one minute past the small hand. Since the big hand travels 12x the speed of the small hand, the big hand would have to back up 5 seconds to be in the same place as the small hand.
2:10
THERES NO ROBOTS IN LORD OF THE RINGS!
god
2ish
IT DONT MATTER LOOK AT UR CELL PHONE
time to get a new clock
at 2 o'clock and 10.909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091 minutes :)
Well? Whose answer is correct?
The speed of the minutes hand is 12 times that of the hours hand.
Both hands have to meet at some point between 2 and 3 o'colock.
Assume minutes hand is at 12, and the hours hand is positioned at 2 (10 minutes). let 12 our reference point, and let our scale to be minutes divisions (60 steps). Both hands will meet at X position from ref. point.
For both hands to mee at X, hours hand will have to move X-10 steps, and minutes hand will have to move X steps.
Speed = Displacement divided by Time, that is, v = d/t, therefore, t = d/v.
Now lets arrange our equations:
V (speed of minutes hand) = 12*v (speed of hours hand)
T (travelling time for minutes hand) = t (travelling tme for hours hand)
X = Distance travelled by minutes hand.
X-10 = Distance travelled by hours hand
since travelling time is the same for both hands => X/V = (X-10)/v
But V=12v , substituting by the previous equation, X/12v = (X-10)/v
=> X/12 = X-10
=> X = 12X-120
=> 11X = 120
=> X = 120/11
=> X = 10.909090909091 steps
Both hand will meet at 10.909090909091 steps(in minutes) from the ref. point (that is 12)
and the time will be approximately 2:10:54 (Hours : Minutes : Seconds)
ali you have way too much time on your hands but i believe your method is correct i wouldve just said 2:11ish cuz im lazy i would say that from 2-3 is divided into fifths (minute marks) and when the little hand moves five ticks (from 2 to 3) the big hand moves 60 ticks (one hour) 60/5=12 so when the little moves 1 the big moves 12 so the big is at the 0 tick (over the 12) the little is at the 10 tick (2o'clock) when the little moves one to the 11 tick the big moves to the 12 tick. they have passed the point of coincideing lets backtrack the big moves back one to the 11 mark and the big moves 1/12 back towards the 10 tick. at his point i would assume that the cuku clock doesnt have a second hand so it would be exactly 2:10 (you wouldnt round up with time) even though it is just shy of 2:11
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