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April 13th, 2018, 12:26 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Working rates with algebra
One day, it takes p hours for q factory workers to construct r items. The following day three more worked join the team and four more items are required to be constructed. 1)Find how many hours it will take, in terms of p,q and r. 2)If in fact it takes the same length of time, find an equation and show that it reduces to 4q=3r. Instead of answering the questions, unless you would like to, can someone please clarify how to express rates of work by algebra, like in this question? Thanks 
April 13th, 2018, 05:05 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,760 Thanks: 860 
Make up a simple example; as example: 5 workers working for 8 hours construct 400 items. So q=5, p=8 and r=400. Which means each worker constructs 400/(5*8 ) = 10 items per hour. Now what happens if (as example) 2 more workers are hired? 7 workers @ 10 items per hour = 70 items per hour. Play with that !! 
April 22nd, 2018, 12:30 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,240 Thanks: 885  Quote:
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Last edited by Country Boy; April 22nd, 2018 at 12:34 AM.  
April 22nd, 2018, 06:59 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,050 Thanks: 430  Quote:
$ p = \dfrac{ p q r}{r(q + 3)} \implies 1 = \dfrac{qr}{r(q + 3)} \implies 1 = \dfrac{q}{q + 3} \implies q + 3 = q \implies 3 = 0.$ It shows how greatly I respect Country Boy that I literally checked my work on that twice. What was going on? I had been following right along, hadn't I? Not carefully enough it turned out. $\dfrac{r + 4}{\dfrac{r(q + 3)}{pq}} = \dfrac{r + 4}{1} * \dfrac{pq}{r(q + 3)} = \dfrac{pq(r + 4)}{r(q + 3)} \ne \dfrac{pqr}{r(q + 3)}.$ $\therefore p = \dfrac{pq(r + 4)}{r(q + 3)} \implies 1 = \dfrac{qr + 4q}{qr + 3r} \implies qr + 3r = qr + 4q \implies 3r = 4q.$  
April 22nd, 2018, 08:26 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,760 Thanks: 860 
Jeffroi, dans le coin pour 12 minutes....

April 22nd, 2018, 08:47 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 1,050 Thanks: 430  
April 22nd, 2018, 08:53 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,760 Thanks: 860 
Oh hokay; but finish off the 4 minutes when you come back....


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algebra, rates, working 
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