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#1 2013-09-27 16:16:56

Fruityloop
Member
Registered: 2009-05-18
Posts: 120

Problems from a book

I have a book which I think has the wrong answers to 2 problems.

In the first problem there are 3 people, we'll call them A, B, and C.

A can make 5 scarves while C makes 2.
B makes 4 scarves while A makes 3.

A's scarf takes 5 times as much cloth as B's scarf.
Three of B's scarves take as much cloth as 5 of C's scarves.

C's scarves are 4 times as warm as B's scarves.
A's scarves are 3 times the C's scarves.

Who's the best overall?
Interestingly, I have 2 books which have this exact same problem, one book is from 1885 and the other book
is from 2013.  I believe that the book from 1885 has the correct answer, it claims that the best overall is C.
The book from 2013 claims the answer is A.  The book from 2013 makes the mistake (which is pointed out
by the older book) of adding the numbers once the proportions are established, when they should be multiplied instead.

The other problem is this, again 3 people A, B, and C.

A and B working together can prepare a shipment in 8 days.
A and C working together can prepare a shipment in 9 days.
B and C working together can prepare a shipment in 10 days.

How long would C take working alone?
The book says 22 days.  I am getting 23 and 7/31 days.


The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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#2 2013-09-27 22:34:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,672

Re: Problems from a book

Hi;

I am getting 23 and 7/31 days.

That is what I am getting also.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-09-28 00:33:16

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,258

Re: Problems from a book

hi Fruityloop,

I don't see how anyone can answer the first question without knowing how much 'weight' we should give to each quality.

Speed of working. The ratio of how many scarves can be made is

A:B:C = 15:20:6.

So for speed of working alone B is best.

How much cloth?  The ratio of how much cloth is

A:B:C = 25:5:3

so if you want economy of material, C is best.

How warm?  The ratio of how warm the scarf is

A:B:C = 12:1:4

so if you want the warmest scarf A is best.

That's what I'd go for, because I'm not bothered about how long they take or how much cloth they use;  I just want to wrap up warm!

But if I were a manufacturing boss and I wanted to employ just one of the three, the other factors would also become important.  I could get more scarves for the wages, if I employ B, but of labour is cheap and materials expensive, I might choose C.

How can you work together three unrelated factors like this?  You could give each factor a weighting to account for how important it is relative to the other factors and then get an overall score for each person.  But the score would depend on the weightings;  what I have said above shows that any could come out on top if the right weighting factor is set.

My conclusion:  There is no absolute solution to this problem.

Bob

Last edited by bob bundy (2013-09-28 00:36:48)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2013-10-09 15:35:52

Fruityloop
Member
Registered: 2009-05-18
Posts: 120

Re: Problems from a book

The other problem is this, again 3 people A, B, and C.

A and B working together can prepare a shipment in 8 days.
A and C working together can prepare a shipment in 9 days.
B and C working together can prepare a shipment in 10 days.

How long would C take working alone?
The book says 22 days.  I am getting 23 and 7/31 days.

That is what I am getting also.

Yeah, I don't understand the solution in the book. They have the following equations...

(A + B)/4 = 8
(A + C)/4 = 9
(B + C)/4 = 10

So, A = 14, B = 18, and C =22.
I honestly have no idea what they're doing.


The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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#5 2013-10-09 15:49:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,672

Re: Problems from a book

Hi;

I am still getting mine and yours. Where does there 4 come from?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2013-10-09 20:46:39

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,258

Re: Problems from a book

hi,

I get that too.  Here's my method and working:

Let's measure the work to be done in 'shipments' = 1

Let A's rate of working be A; similarly B and C.

Adding

What is the book doing?  Let's see .....

Since we know 8 is a time in days

That looks like complete nonsense to me.  shame

Sometimes books have misprints, but this is too far removed from correct mathematics to be that as far as I can see.  Coupled with what I've already said about the other question my recommendation is this:

Get another book!

smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2013-10-09 22:27:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,672

Re: Problems from a book

Hi;

Get another book!

I am afraid I must agree.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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