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#1 2005-07-11 17:04:10

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,206

Two cyclists

Two cyclists A and B go in circles,
A takes 1 hour to complete one circle,
and B completes 6 circles (the same circle as A) in an hour.
The question is, if the two start, in the same direction at
07.30 AM, when would they next cross each other?:)


Character is who you are when no one is looking.

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#2 2005-07-11 19:49:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

Put in in the form of an equation. So,
[Ma loo ga wooga]

And all that means that they will next cross at [blah blah]
See, simple!:D


Why did the vector cross the road?
It wanted to be normal.

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#3 2005-07-11 20:59:20

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

I think that by the time B has gone once around, A will have gone 1/6th around, then B just has to go that 1/6th further to catch A, but by then A will have moved further ... oh no, will he ever catch A?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2005-07-11 23:29:30

ganesh
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Registered: 2005-06-28
Posts: 15,206

Re: Two cyclists

MathsIsFun wrote:

... oh no, will he ever catch A?

Reminds me of Zeno's Paradoxes!
B is faster than A and would get past him eventually!


Character is who you are when no one is looking.

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#5 2005-07-11 23:32:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

That's what I was thinking!
zeno-a&t.jpg
big_smile


Why did the vector cross the road?
It wanted to be normal.

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#6 2005-07-12 19:09:40

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,206

Re: Two cyclists

Speed = Distance travelled / Time taken

Let the distance travelled in 1 circle be C Units.
Speed of A = C Units/hour and Speed of B=6C Units/hour.

Last edited by ganesh (2005-07-12 22:08:10)


Character is who you are when no one is looking.

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#7 2005-07-12 20:52:22

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

I got that, but edited it after about 2 minutes.


Why did the vector cross the road?
It wanted to be normal.

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#8 2005-07-12 21:36:53

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,206

Re: Two cyclists

Maybe, I should have waited for some more days
before giving the solution.


Character is who you are when no one is looking.

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#9 2005-07-12 21:38:14

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

Or even longer ... give all visitors a chance.

(Wow, B DOES get past A ! smile )


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2005-07-12 21:53:11

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

Is it possible to use BBCode to make 'invisible writing' that you need to copy and paste to read?
Just a thought.


Why did the vector cross the road?
It wanted to be normal.

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#11 2005-07-13 00:04:44

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

The text could be the same colour as background ... I could delve into PunBB code to see if that is possible.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#12 2005-07-13 00:07:19

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

Would it work even though it's possible to have different 'visual styles' and hence different coloured backgrounds?


Why did the vector cross the road?
It wanted to be normal.

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#13 2005-07-13 00:26:03

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

It may or may not be hard, depending on whether I can apply the "current" background style to the text. I won't know till I have a look.

And I don't know how to extend BBCode, but there should be a way.

Hmmm ... what would we call the BBCode?  [ ??? ]


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#14 2005-07-13 03:41:15

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

Re: Two cyclists

Call it? YAY!!!!!! Another name-making-up thingy! (the last was for the new board)


School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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#15 2005-07-13 08:44:29

Zach
Member
Registered: 2005-03-23
Posts: 2,075

Re: Two cyclists

You can do it in PHPBB, so I expect it's possible on PunBB. Perhaps editing the CSS, if you can?


Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

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#16 2005-07-13 09:57:00

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

Probably a combination of code and CSS. I will have a look in a coupla days.

Name Idea: whisper


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#17 2005-07-14 16:44:39

tt
Member
Registered: 2005-07-03
Posts: 32

Re: Two cyclists

They will cross each other at 7:42AM.

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#18 2005-07-14 19:03:04

justlookingforthemoment
Moderator
Registered: 2005-05-26
Posts: 2,161

Re: Two cyclists

shadow

or

silhouette

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#19 2005-07-14 19:34:20

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Two cyclists

I like those names.

Apparently the search engines HATE invisible text because spam sites use it to misdirect people to their site. You know, mention important words several times at the bottom of the page even if it isn't part of the site. So advise I have seen said you can be banned by the search engines for using it.

So, I have thought "what about just hard-to-read text?" You know it is there, so no deceit, but you have to run your mouse across it to read it or something.

So maybe White Text or some clever "CSS" stuff.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#20 2005-07-14 19:37:32

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Two cyclists

It's that kind of thing that makes Tony Blair's site a top hit in a google search for 'Liar' and George W Bush's site a top hit in a google search for 'miserable failure'. It only works with google though, because they search in a different way to all other search engines.

Also, some of the 'visual styles' display text as white anyway, so that wouldn't always work.


Why did the vector cross the road?
It wanted to be normal.

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