September 15th, 2019, 09:04 AM  #1 
Newbie Joined: Jan 2017 From: London Posts: 18 Thanks: 0  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? 
September 15th, 2019, 09:30 AM  #2 
Senior Member Joined: Aug 2012 Posts: 2,412 Thanks: 754 
y, by symmetry. There's no difference between x and y in this question.

September 15th, 2019, 11:11 AM  #3 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
Doesn't match the physics of the problem, though. $(x~men)(x~hr/dy)(x~dy)=x^3~manhours$. Let $a = f(mh)$ be the number of articles produced. Theoretically, it should be proportional to manhours. $a = r \cdot mh$ $x = r \cdot x^3$ 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 manhours. 2 articles in this time means r = 0.25 articles/manhour. (5 men)*(5 hr/dy)*(5 dy) = 125 manhours (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. 
September 15th, 2019, 11:43 AM  #4 
Newbie Joined: Jan 2017 From: London Posts: 18 Thanks: 0 
I've attached the scanned question q.8

September 15th, 2019, 12:34 PM  #5 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
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, outofplane 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.) 
September 15th, 2019, 02:30 PM  #6  
Newbie Joined: Jan 2017 From: London Posts: 18 Thanks: 0  Quote:
 
September 15th, 2019, 03:19 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,304 Thanks: 961 Math Focus: Wibbly wobbly timeywimey stuff. 
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 
September 16th, 2019, 05:11 AM  #8 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
You've never heard of a family with 2.3 children? They grew up and started working.

September 16th, 2019, 01:14 PM  #9  
Senior Member Joined: Aug 2012 Posts: 2,412 Thanks: 754 
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:
 
September 17th, 2019, 12:33 AM  #10  
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 132 Thanks: 49 Math Focus: Area of Circle  Quote:
Last edited by skipjack; September 17th, 2019 at 08:05 AM.  

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