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 February 27th, 2014, 08:38 PM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18 women and bags Question 1(a) Sandra can make a bag in 2 minutes. She calls 7 of her friends who also work at the same rate (a bag in 2 minute). How long will it take them to make 1200 bags? My attempt: There are 8 people. If they all start working at the same time, at the end of 2 minutes there will be 8 bags. The rate = $\frac{2 minutes}{8 bags}=\frac{1 minute}{4 bags}$ To make 1200 bags the time required = $\frac{1 minute}{4 bags}\times 1200 bags=300 minutes$ Question 1(b) If Sandra called only 3 friends who work at the following rates: 1 bag in 3 minutes, 1 bag in 4 minutes and 1 bag in 5 minutes then, together how long will it take to make 1200 bags? My attempt: LCM (2, 3, 4, 5) = 3 x 4 x 5 = 60 minutes In 60 minutes Sandra makes 60/2 = 30 bags In 60 minutes friend 1 makes 60/3 = 20 bags In 60 minutes friend 2 makes 60/4 = 15 bags In 60 minutes friend 3 makes 60/5 = 12 bags So the rate = $\frac{60 minutes}{(30+20+15+12)bags}=\frac{60 minutes}{77 bags}$ Therefore time taken to make 1200 bags = $\frac{60 minutes}{77 bags}\times 1200 bags= 935 minutes$ Is my approach to the problem correct? Is the answer correct? Is there a better way to solve this problem? Thanks
 February 27th, 2014, 08:53 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,637 Thanks: 959 Math Focus: Elementary mathematics and beyond Re: women and bags $\frac12x\,+\,7x\,=\,1200\,\Rightarrow\,x\,=\,160\, \Rightarrow\,\text{Time required: 2 hours and 40 minutes.}$
February 27th, 2014, 09:05 PM   #3
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Re: women and bags

Quote:
 Originally Posted by greg1313 $\frac12x\,+\,7x\,=\,1200\,\Rightarrow\,x\,=\,160\, \Rightarrow\,\text{Time required: 2 hours and 40 minutes.}$
I didn't understand how you got the equation.

February 27th, 2014, 09:28 PM   #4
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Re: women and bags

Quote:
Originally Posted by shunya
Quote:
 Originally Posted by greg1313 $\frac12x\,+\,7x\,=\,1200\,\Rightarrow\,x\,=\,160\, \Rightarrow\,\text{Time required: 2 hours and 40 minutes.}$
I didn't understand how you got the equation.
Sandra = 1/2 bag in 1 minute : (1/2)x
7 friends = 1 bag each in 1 minute: 7x

 February 27th, 2014, 09:37 PM #5 Senior Member     Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18 Re: women and bags Thanks Denis and greg1313. I made a mistake in Question 1(a). All the friends work at the same rate (1 bag in 2 minutes). SORRY for wasting your time there. What about question 1(b)? Can you have a look.
 February 27th, 2014, 11:07 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,140 Thanks: 1415 For 1(b), why round down? They can't quite finish 1200 bags in 935 minutes. In 936 minutes, they can finish 1201 bags (and the friend who makes a bag in each 5 minutes would have had time to work for 1 minute on the 1202nd bag).

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