### Author Topic: Two ants on a clock  (Read 9075 times)

#### MrPuzzle

• Jr. Member
• Posts: 75
##### Two ants on a clock
« on: 七月 13, 2004, 01:59:27 pm »
The problem with this forum is that we don't have enough participants. If everyone of us forward this forum to other forums that s/he visit, we will get some new comers, and the forum will become more interesting. (It is pretty interesting already).

Here's a problem I just saw two days ago, it is not hard, don't require any creative thinking at all, I just thought among all those clock related problems, this is a more interesting one.

-----original problem----------------
Two ants are on a clock-face at midnight.  One ant is at the 12 and one is
at the 6, and are separated by a distance of 2r. (The ant at the 12 can
step immediately onto the second-hand.) Each ant has a maximum walking
speed of r/minute.

How would each ant travel in order for them to meet in the least elapsed
time?  Where would they meet, and at what time?

-------------------------

My comments: Obviously, if the two ants ignore the second-hand, and walk straight to the center, it will take them 60 second to meet.  If the ant at the 12 immediately step on to the second-hand, and the second ant sits still, it will take them 30 seconds to meet.  If instead of sitting still, the second ant start to walk along the big circle, it will take them about 25.88 second to meet.  Is there any other way for them to meet in less time? Is it possible for the first ant to step out of the second-hand at some point and save time? What is the least amount of time you can find?

#### packman

• Full Member
• Posts: 226
##### Two ants on a clock
« Reply #1 on: 七月 13, 2004, 02:18:45 pm »
If it is a clock, it is more than likely be put up vertically. The ant at 12 just release its grasp and let itself fall. The time is 2*sqrt(r/g).
Unless the clock is huge......This is the fastest way to meet.
The ant at 6 could climb up a bit to save some time, but it's not worth it. It's hard for a falling ant to grasp the surface...

#### packman

• Full Member
• Posts: 226
##### Two ants on a clock
« Reply #2 on: 七月 15, 2004, 09:33:20 am »
If the image is not shown, see http://www.geocities.com/packman_at_cnd/math_problems/ant.html
For some reasons, even if you click the above link, it says "page not found". Please open a new browser window and type in the URL. (I don't know why. ??)
Or you can right-click the broken image -> view image (or download to disk)