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## #1 2011-07-24 23:55:13

djohnstone3
Member
Registered: 2011-07-24
Posts: 2

### Band around the Earth

I have a problem with the solution!  When the solution is stated they subtract formulas, but the original formula is in kilometers and the "added" measurement is in meters.  Instead of 10, shouldn't it read .01.

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## #2 2011-07-25 00:01:55

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Band around the Earth

hi djohnstone3

welcome to the forum.

you are probably right but it would be nice if you could post the problem here.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2011-07-25 00:16:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Band around the Earth

Hi djohnstone3;

Welcome to the forum!

Where is the problem?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #4 2011-07-25 00:20:00

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Band around the Earth

hi Stefy

I think it's this one

http://www.mathsisfun.com/puzzles/band-around-the-earth.html

to djohnstone3

The solution uses R without specifying units, so they could be meters.

When you subtract those units (whatever they are) all disappear leaving a formula for the gap, again no units specified.

So if you substitute a value of 10 meters the answer will be in meters.

Confused?

My friend is 5 feet 8 inches tall.
I am 5 feet 6 inches tall.

How much taller is my friend?

5 feet 8 inches - 5 feet 6 inches = 2 inches.  I don't have to change the feet to inches to do this.

Bob

Last edited by bob bundy (2012-01-09 06:38:52)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2011-07-25 00:32:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Band around the Earth

hi bob

yes you are right.you could express it in km but it wouldn't change anything cuz the stuf in kilometres cancels out.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #6 2011-07-25 23:42:15

djohnstone3
Member
Registered: 2011-07-24
Posts: 2

### Re: Band around the Earth

You do have the correct problem.  The error occurs when the solution uses 10 kilometers as the added distance, when in fact the added distance is .01 kilometers.

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## #7 2011-07-26 02:12:16

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Band around the Earth

hi djohnstone3

Did you read my earlier post?

10 = 2 × pi × Gap

So, the Gap = 10 / (2 × pi) = 1.6m

That looks like 10 meters to me.

If you're still not convinced try converting all measurements into Km.

You'll get an answer of 0.0016 Km

Bob

Last edited by bob bundy (2011-07-26 02:15:57)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #8 2012-01-09 06:28:58

Jasquith
Member
Registered: 2012-01-09
Posts: 2

### Re: Band around the Earth

Hi all,
Just had a crack at the Band Around the Earth problem. I get the right answer, but using a different method. I don't understand how the following subtraction occurs in the example given:

Before: Original Circumference = 2 × pi × R
After: Original Circumference + 10 = 2 × pi × (R + Gap)

to give: 10 = 2 × pi × Gap

The main problem that I have is that one cannot divide R out of the equation as it is added to Gap, nor can it be subtracted as it is multiplied by 2 pi.

If someone could explain this to me I'd be very grateful! Just to give some more info, my solution works by substituting the following two equations together:

R + Gap = 40,000,010 / 2 x pi
R = 40,000,000 / 2 x pi

to give:

(40,000,000 / 2 x pi) + Gap = 40,000,010 / 2 x pi

and thus:

Gap = (40,000,010 / 2 x pi) - (40,000,000 / 2 x pi)
The answer comes out in metres.

Many thanks in advance to anyone who can help!
John

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## #9 2012-01-09 06:35:03

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Band around the Earth

hi Jasquith

The earlier answers are just algebraic versions of your (partially) number solution.

Put C = 40 000 000 and the two come to the same thing.

Bob

Last edited by bob bundy (2012-01-09 06:35:50)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #10 2012-01-09 23:55:33

Jasquith
Member
Registered: 2012-01-09
Posts: 2

### Re: Band around the Earth

Hi Bob,

Thanks for your reply. All clear now!

John

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## #11 2012-04-03 18:50:26

anky2930
Member
Registered: 2012-03-27
Posts: 21

### Re: Band around the Earth

hi djohnstone3,
welcome to the forum. We need the question at least so that we can give answer.

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## #12 2012-04-03 18:55:24

bob bundy
Registered: 2010-06-20
Posts: 8,108

### Re: Band around the Earth

hi anky2930

I think he meant

http://www.mathsisfun.com/puzzles/band- … earth.html

and I think this was answered at the time.

Have a look and decide for yourself.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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