I have a simple question from my simple mind.
I checked my watch at noon, and notice the big hand and the little hand are exactly in sync.
What time will it be next when this happens again?
1:01?
Slightly after 1:05 and 27 secs.
1:05
1:05:05
Every 65 minutes.
1:05:05
Every 65 minutes.
Jabba is close, however I need the exact time.
I’m anal that way.
-Ace
Jabba’s got it. 1:05 would be close, but when the minute hand reaches the 1 (i.e., five minutes past), the hour hand will have moved ahead slightly.
The minute hand will align with the hour hand eleven times in a twelve-hour period (minute hand makes twelve revolutions, while the hour hand makes one: 12 - 1 = 11). The number of seconds in twelve hours is 12 x 60 x 60 = 43,200. Divide by eleven to get 3927.2727 (repeating decimal). 3927 seconds is 65 minutes, 27 seconds, plus the .2727&c second left over = 1:05:27.27.
The mods may now close this thread. 
Jackelope. Very good, but still not correct.
Fix your “plus left over, and you’ve got the answer.” Your answer must be in the form of H:M:S:etc:
Incidently, kudos to you for finding the easy route. A summation of a exponential sequence of 1/12 + 1/12^2 + 1/12^3 will also lead you to the same point.
:smack:
Jesus almighty, 1:01???
All right, who hijacked my computer and posted that crap?
ROFLMAO! So much for everyone ignoring it, eh?
No worries, we’ve all been there.
-Ace
If you need a hint, Jackelope, how many femto-seconds will it be? pico-seconds?
I’m back. You want it in the form of H:M:S:etc.? What are the units of “etc.”? How about this: 1:05:27 3/11 (i.e., 27 and 3/11 seconds). A perfectly precise answer, which of course assumes a perfectly calibrated watch.
Oh, wait, now I see what you mean; I had left it as “1:05:27.27.” Please place a “repeat bar” (what’s that called?) over the final 27, though I’m more comfortable with the elegance of the fraction as written above.
And thanks for the kudos, but I’m always one to look for the easy way; if I’d done it the hard way, I’d feel it was deserved.
As long as we’re (tangentially) on the subject of various methods of problem-solving, I have a question:
In my high-school physics course, we were given a problem in which a ball is jettisoned horizontally from the top of a flight of stairs, each stair having equal height and depth. Our task was to determine which stair the ball would land on (all units were included, though they are now lost in the mist). My solution, which seemed obvious, was to chart the parabola of the ball’s trajectory and find out where it intersected with the simple x = -y line of the stairs, and presto. So I figured it out, and gave it to the teacher, who was impressed and said it “hadn’t ocurred to him to solve it that way.”
My question is this: How ELSE would you solve it? Here I am 13 years later, and it still bothers me because I frankly can’t think of any other way to figure this out, short of the somewhat vulgar method of actually building some stairs and kicking a ball off of them.
Any help?
My bolding.
It will be noon again in 24 hours, so the answer is “Noon”
Ha! The mathematician foiled (in several senses) by the grammarian!
High-five from an English major! 
1:05:27 and 3/11 seconds is perfectly acceptable.
Consider these further bonus points then:
- Answer in the form of :H:M:S:S/60:S/3600:…:
- How many femtoseconds? Pico seconds?
- Can you give a formula to quickly find out the above?
-Ace
BTW, well done, Jackelope!!
[Balloons drop from above]
Friggin’ english majors!!! :rolleyes: