AIME I Problem 2 2007

[zefuri]

A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 8 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.

[Michael T]

How come I didn't see this problem sooner?

Okay, we have three possible cases: Either Al, Bob, or Cy is in the middle. Since Bob is walking the fastest and Cy starts the latest, we might as well start by seeing if Al is in the middle. Where [unparseable or potentially dangerous latex formula] is the time elapsed since Al started on the walkway, we have:

[unparseable or potentially dangerous latex formula]

Which yields [unparseable or potentially dangerous latex formula]

To make sure Al is in the middle, we check all three cases.

[unparseable or potentially dangerous latex formula]

Which yields [unparseable or potentially dangerous latex formula] which opaquely is not true.

[unparseable or potentially dangerous latex formula]

Which yields [unparseable or potentially dangerous latex formula] which is opaquely before Bob or Cy started walking. Therefore, by process of elimination, we gather that Al is in the middle at [unparseable or potentially dangerous latex formula]. At this time, Al has traveled [unparseable or potentially dangerous latex formula]

[zefuri]

This problem was tricky because a lot of people didnt see beside the walkway.

[zefuri]

opaquely?..wth

[NickR]

Rofl at "opaquely" and that problem was really easy...o.O (of course it is #2)

[zefuri]

what a nubcake i dont even know how opaquely has to do with anything

[Quelloquialism]

[zefuri]

ohh i didnt even know that that was supposed to be clearly -__-

[Quelloquialism]

My gosh, you people.

http://www.m-w.com/

OPAQUELY IS AN ANTONYM OF CLEARLY.

...lemme guess you guys are going to be rejected from college for getting 200's on the Crit. Reading section of the SAT? =D

[zefuri]

IM really really good at SATing...

and yes i knew opaquely was an antonym but i didnt think that clearly went htere
-_-

[Englandude]

[zefuri]

obviously the plural of moose goshhh havent been studying for the SATs i see...

[Englandude]

Ooo. Haha. SAT huh? I hate the SAT. Its booorrrrrring.

[Englandude]

[Englandude]

You know what....why don't you pick on people your own height?

[zefuri]

no ones that short...

[Englandude]

I was just kidding buddy. I've never seen you so i don't know if you are short. LMAO. Woooo....There is a girl in my grade who is like 4 and a half feet tall. It's quite funny...... =D

[Englandude]

O. Are you tha short kid in the middle? HAHAHA. LMAO!!!

[zefuri]

hes 4 ft tall...and hes in 10th grade...you do the math

[Englandude]

Haha. Maybe you should consider eating more vegetables or something. Lol. J/K.
4ft tall....10th grade.....that leaves me speechless. WOOOOOOO....HAHAHAHA.

[zefuri]

hes typing nubcake

[Englandude]

Thank you zefuri. You make a great point. I am typing. Not talking. So HAH!!! I win i win i win. Own me in everything huh? Lets see, if i played you in pool, i would win. If we played one on one in b ball, i would win. If we played golf, i would win. If we played tennis, you guessed it, i would WIN.

[Englandude]

I beg to differ. It's on. Me and you have to have a little friendly competition one of these days. You definetly can't beat me at pool. I don't know y u think u can. You definetly can't beat me at b ball. (Height makes a difference.) =)

[Englandude]

I'm 5 foot 11. Almost 6 foot. If i just eat my vegetables.....

[Englandude]

Yeh...sure...if ya wanna say it like that. Why not?