February 29th, 2012, 05:58 AM  #1  
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Rate problem Quote:
R = rate of Orcs E = rate of Elves H = rate of Humans (13*R)(7) + (7*E)(7) = 1 (Rate of 13 Orcs) * (7 days) + (Rate of 7 Elves) * (7 days) = 1 Tower 91R + 49E = 1 (6*E)(6) + (13*H)(6) = 1 (Rate of 6 Elves) * (6 days) + (Rate of 13 Humans) * (6 days) = 1 Tower 36E + 78H = 1 I set the equations in terms of Orcs and Humans so I could work with everything in terms of Elves: R = (1  49E) / 91 H = (1  36E) / 78 So the (rate of Elves)(time) + (rate of Orcs)(time) + (rate of Humans)(time) = 1 Tower: (E)(t) + [(1  49E) / 91](t) + [(1  36E) / 78](t) = 1 Simplified to get rid of the fractions (multiply by 546 since that's the LCD): (546E)(t) + (6  294E)(t) + (7  252E)(t) = 1 I have 2 variables here so I'm not sure how to solve for 't' because I don't know each individual rate. I'm supposed to solve this in ~3 minutes yet I spent like 30 on it  
February 29th, 2012, 06:24 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Rate problem
From the first equation, we have that IN ONE DAY (sorry for the emphasis, but it's necessary!) 13 orcs and 7 elves can build 1/7 of a tower. Likewise, in ONE day, 6 elves and 13 humans can build 1/6 of a tower. Adding all that up, in ONE day, 13 orcs and 13 elves and 13 humans can build 1/7 + 1/6 = 13/42 of a tower. So dividing by 13 gives 1 day > 1 orc + 1 elf + 1 human building 1/42 of a tower. 42 days > 1 tower. 
February 29th, 2012, 06:26 AM  #3 
Member Joined: Dec 2011 Posts: 61 Thanks: 1  Re: Rate problem
A simpler way (not to chaz) would be: Adding the equations gives so the no. of days 
February 29th, 2012, 06:52 AM  #4 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Rate problem
Dangit. Maybe I should pursue a degree in something other than mathematicsrelated if I'm having trouble with Algebra I in college, lol...I can do everything except word/application problems (interestingly enough I find quadratic applications MUCH more easier than linear applications)

February 29th, 2012, 07:23 AM  #5  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Rate problem Quote:
Don't be discouraged!  
February 29th, 2012, 07:56 AM  #6  
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Rate problem Quote:
 
February 29th, 2012, 07:59 AM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Rate problem Quote:
Nonword problem: 3a + 2b = 1.15 2a + 3b = 1.10 Word problem: Peter Jr. , son of Peter Sr. , bought 3 apples and 2 bananas for $1.15. Let it be known that if he had bought 2 apples and 3 bananas instead, it would have cost him a nickel less.  
February 29th, 2012, 09:07 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Rate problem
Yet another way: In 42 days, 13 Orcs, 13 Elves, and 13 Humans working together can build 13 towers, so in 42 days 1 Orc, one Elf and 1 Human can build 1 tower. 
March 1st, 2012, 12:04 AM  #9  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Rate problem Quote:
 
March 1st, 2012, 12:07 AM  #10  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Rate problem Quote:
 

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