Elementary POW, March 31-April 4, 1997
Elem POW Problems || March - June '97 Problems || Elem POW Main Page
Suppose a group of you are going to walk to a blue wall 100 meters away. Each person will travel only a certain fraction of the remaining distance for each turn. One person will go only 1/4 of the way each turn. The second will go 1/3 of the way, and the 3rd person will go 1/2 of the distance each turn.How long will it take each person to actually reach the wall? (No hands!)
This week's mentors were Tracey Jensen and her homeschooled students from Oklahoma.
Subj: P.O.W
Date: 97-04-07 15:28:49 EDT
From: bcoulter@teaparty.terc.edu (Bob Coulter)
To: castforem@aol.com
We decided that none of the people could get to the wall. They would
always have a piece left.
Example:
100/2 = 50 50/2 = 25 25/2 = 12.5 12.5/2 = .25 6.25/2= 3.125
You see you will never get to the wall.
This problem was solved by:Jackie Breckinridge, Justin Weiss, Brian
Powers, Nathan Strauss, and Ariel Franks.
Forsyth School St.Louis Mo Bob Coulter's math class
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Problem Of The Week
Date: 97-04-07 15:28:58 EDT
From: JKAT9@aol.com
To: castforem@aol.com
My name is Julia Tomasko and I live in Washington DC. I am in fourth
grade at Gorgetown Day School and my teacher is Paul Nass.
The answer I got to the problem of the week was that none of the
people would ever reach the blue wall. The way I figured it out was I
made 100 little boxes with each little box representing one of the
meters. And then I made a mark in the meters that the first second
and third people went in. But after I did this a couple of times I
realized that none of the people would get to the end. The person who
went 1/4 of the remaining distance would never get there because he
would only go 1/4 of the way that was left each time and there would
always be 3/4 of the distance that was left after the last turn
between him and the wall. The person who went 1/3 of the remaining
distance wouldn't get there either because there would always be 2/3
of the distance that was left at the end of the last turn between him
and the wall. And the person who went 1/2 of the remaining distance
wouldn't get to the wall because there would always be 1/2 of the
distance that was left after the last turn between him and the wall.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: POW March 31 - April 4
Date: 97-04-07 15:38:22 EDT
From: chayes@jeffco.k12.co.us (Connie Hayes)
To: castforem@aol.com
Mrs. Hayes
4th Grade
Eric & Tristan
Shaffer Elementary
Littleton, CO
chayes@jeffco.k12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Math
Date: 97-04-07 15:38:52 EDT
From: zampol@woodward.Edu (Beth Ann Zampol)
To: castforem@aol.com
The people will never get to the wall in theory. Technically, they
will always have something left over. In real life they could get
there in time, but mathematically they will never get there because it
would go on forever.
Todd and Katie, Sixth Grade, Mrs. Zampol, Woodward Academy
Beth Ann Zampol
zampol@woodward.edu
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: POW March 31
Date: 97-04-07 15:38:59 EDT
From: bart@pil.net
To: castforem@aol.com
Luke Zarko
Titus Elementary School
Mrs. Bartosiewicz - 4th Grade
Warrington, Bucks County, PA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Problem of the Week
Date: 97-04-07 15:39:02 EDT
From: poconnor@bucksnet.bciu.k12.pa.us (Peggy O'Connor)
To: castforem@aol.com
Names: Jill Smith, Nicole Dowling, Daniel Sullivan, Rachael Caron
Grade: 4
School: Titus Elementary School, Warrington, PA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: POW March 31- April 4, 1997
Date: 97-04-07 15:41:59 EDT
From: vinaya@ibm.net (Vinay K. Aggarwal)
To: castforem@aol.com
Student: Vinay Aggarwal
Teacher: Paul Nass
School: Georgetown Day School, Washington D.C.
Grade: 4th
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: POW
Date: 97-04-07 15:43:24 EDT
From: pchau@ga.k12.pa.us (Phy Chauveau)
To: castforem@AOL.COM
Dear Mrs. Carver,
We have had a lot of fun solving your puzzle. We have come to the
conclusion that no one will ever reach the wall. If person number
three keeps going half of the distance to the wall person number
three will never make it because if you keep dividing something in
half you will never actually make it to zero. The same thing would
always happen for the other people. Thanks for the puzzle.
Sincerely,
Craig Cramer, Sara Wyszomierski, and Cory Ricci
Phy Chauveau
Fifth Grade Teacher- Grade Level Coordinator
Germantown Academy
Fort Washington, PA 19034
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: pow 3/31-4/4
Date: 97-04-07 15:43:31 EDT
From: jrummel@madison.k12.wi.us (John Rummel)
To: castforem@aol.com
This response is from a group of 5th graders in Mrs. Dunlap's class,
Emerson Elementary, Madison, WI.
We think that none of them will ever _actually_ reach the wall
because when you take a half away from something (the distance), you
always have something left. If you keep reducing the distance by a
half, you'll have half left. Even though you'll get very, very close
to the wall, you'll never actually reach the wall.
Nick Bomkamp
Alyxe Smith
Jennifer Buckingham
Mary Cass
Andrea Olson
Mrs. Dunlap's 5th Grade
Emerson Elementary
Madison, WI
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Elementary POW (3/31-4/4)
Date: 97-04-11 11:07:35 EDT
From: glockwoo@monroe.k12.nj.us (Glenn Lockwood)
To: castforem@aol.com
When I tried the Elementary POW, I got it would take infinity turns
to reach the wall. Here is what I got-
PERSON DISTANCE
100m
1st 75m left
2nd 50m left
3rd 25m left
1st approx 6 1/3 left
2nd approx 2 left
3rd approx 1 left
1st approx 3/4 left
2nd approx 2/4 left
3rd ...and it goes on and on...
AS you see, it keeps going into fractions, and fractions, and even
more fractions. It never ends!
Solution by:
Glenn Lockwood, 6th grade
Ms Budrewicz
Brookside School
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Solution to most recent POW March 31-April 4, 1997
Date: 97-04-09 11:53:40 EDT
From: mattzuch@sbceo.k12.ca.us (matt zuchowicz)
To: castforem@aol.com
Ruth-
Some students and I were discussing the solutions to this problem of
the week, and we feel the answer is that the people will never reach
the wall, because each time they walk, they will only walk a half of
the way. For example, the person who walks a 1/2 of the distance,
will walk to the 50 meter mark, then the 25, then the 12.5, then the
6.25, etc., etc. Each time the distance will decrease by half and
therefore will never equal zero. Thus the people will never reach
the end of the wall. Now, after solving it thus, we were afraid that
maybe we misread the problem. Did we?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subj: Problem of The Week 4-3-97
Date: 97-04-07 15:26:46 EDT
From: freemanc@newtrier.k12.il.us (Chris Freeman)
To: castforem@aol.com
KYLE JOHNSON
DAVID NASH
DANIEL ZWELL
MIKE HORN
JEFF CASAS
GRADE 6
MRS. FREEMAN
Highcrest
The people will never reach the wall because they will keep going
1/4, 1/2, or 1/3 of the way left. They'll keep going smaller and
smaller distances (too small to measure or for a person to move). For
example 0.000000000000000000000000000000001 cm.
[Privacy Policy] [Terms of Use]
Home || The Math Library || Quick Reference || Search || Help
The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.