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September 15th, 2019, 09:04 AM   #1
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Algebraic Puzzle

If x men working x hours a day for x days produce x articles (not necessarily a whole number of articles) find out how many articles are produced by y men working y hours a day for y days

Can anyone help in how to approach this?
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September 15th, 2019, 09:30 AM   #2
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y, by symmetry. There's no difference between x and y in this question.
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September 15th, 2019, 11:11 AM   #3
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Doesn't match the physics of the problem, though.
$(x~men)(x~hr/dy)(x~dy)=x^3~man-hours$.

Let $a = f(mh)$ be the number of articles produced. Theoretically, it should be proportional to man-hours.
$a = r \cdot mh$
$x = r \cdot x^3$ suggests $r = x^{-2}$.

Thus, $\displaystyle f(y^3) = \frac{y^3}{x^2}$.

Example: x = 2, y = 5.
2 men*2 hours a day*2 days = 8 man-hours. 2 articles in this time means r = 0.25 articles/man-hour.
(5 men)*(5 hr/dy)*(5 dy) = 125 man-hours
(0.25 art/mh)*(125 mh) = 31.25 articles

tl;dr: The problem doesn't make sense if postulated "for all x," implying x is a particular value that happens to make the statement true.
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September 15th, 2019, 11:43 AM   #4
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I've attached the scanned question q.8
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File Type: jpg 20190915_201426.jpg (90.4 KB, 15 views)
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September 15th, 2019, 12:34 PM   #5
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I'm sticking with my answer. It fits the question and also the theme of polynomial expressions in the neighbouring questions.

Also, pet peeve of mine, but, "scanned," and, "photographed," are not the same things. Scanned images tend not to have as much distortion, out-of-plane focus issues, and shadows of your cell phone on top of them. (Educating the next generation before they come to uni and have us ask for scanned documents in their projects and lab reports.)
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September 15th, 2019, 02:30 PM   #6
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Quote:
Originally Posted by DarnItJimImAnEngineer View Post
Doesn't match the physics of the problem, though.
$(x~men)(x~hr/dy)(x~dy)=x^3~man-hours$.

Let $a = f(mh)$ be the number of articles produced. Theoretically, it should be proportional to man-hours.
$a = r \cdot mh$
$x = r \cdot x^3$ suggests $r = x^{-2}$.

Thus, $\displaystyle f(y^3) = \frac{y^3}{x^2}$.

Example: x = 2, y = 5.
2 men*2 hours a day*2 days = 8 man-hours. 2 articles in this time means r = 0.25 articles/man-hour.
(5 men)*(5 hr/dy)*(5 dy) = 125 man-hours
(0.25 art/mh)*(125 mh) = 31.25 articles

tl;dr: The problem doesn't make sense if postulated "for all x," implying x is a particular value that happens to make the statement true.
I was actually thinking along these lines too but then realised that it cannot work for any value of x. The relationship between x and y is r (0.25) really but this could be different for different x's
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September 15th, 2019, 03:19 PM   #7
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My problem is that the problem starts with "x workers" producing "x articles" and that x is "not necessarily a whole number of articles" meaning that the number of workers may also not be a whole number!

I'm thinking this problem is either seriously badly written or that there a massive typo.

-Dan
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September 16th, 2019, 05:11 AM   #8
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You've never heard of a family with 2.3 children? They grew up and started working.
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September 16th, 2019, 01:14 PM   #9
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What's the latest consensus? I admit I could never get through a grade school math curriculum these days.

If we assume that they mean that this is true for one particular value of x, does the question make more sense? I couldn't quite follow the earlier exposition. I'd be interested in seeing a clear explanation of this problem. I agree that because they printed this in a text, they must mean for you to do some kind of calculation.

There is an old story.

Quote:
Schoolmaster: Suppose x is the number of sheep in this problem

Pupil: But, Sir, suppose x is not the number of sheep

(I asked professor Wittgenstein if this is not a profound philosophical joke, and he said it was.)
https://philosophy.stackexchange.com...ein-joke/53439
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September 17th, 2019, 12:33 AM   #10
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Quote:
Originally Posted by topsquark View Post
My problem is that the problem starts with "x workers" producing "x articles" and that x is "not necessarily a whole number of articles" meaning that the number of workers may also not be a whole number!

I'm thinking this problem is either seriously badly written or that there a massive typo.

-Dan
Actually, the number of workers can be non-integer, even complex number, depending on the universe.
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Last edited by skipjack; September 17th, 2019 at 08:05 AM.
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