My Math Forum Rate problem

 Algebra Pre-Algebra and Basic Algebra Math Forum

February 29th, 2012, 06:58 AM   #1
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Rate problem

Quote:
 13 Orcs and 7 Elves can build a tower in 7 days. 6 Elves and 13 Humans can build a tower in 6 days. How many days does it take for 1 Orc, 1 Elf, and 1 Human to build a tower? (Constant rate)
First I set variables for each of the rates:

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, 07:24 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5 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, 07:26 AM #3 Member   Joined: Dec 2011 Posts: 61 Thanks: 1 Re: Rate problem A simpler way (not to chaz) would be: $13O+7E=\frac{1}{7}$ $6E+13H=\frac{1}{6}$ Adding the equations gives $13(O+E+H)=\frac{13}{42},$ $O+E+H=\frac{1}{42}$ so the no. of days$=42$
 February 29th, 2012, 07:52 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 mathematics-related 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, 08:23 AM   #5
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Re: Rate problem

Quote:
 Originally Posted by daigo Dangit. Maybe I should pursue a degree in something other than mathematics-related 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)
That's no way to talk! Sometimes students first hire me (as a tutor) when they are on their third OR FOURTH try at College Algebra. Of course, I blame the teachers somewhat...

Don't be discouraged!

February 29th, 2012, 08:56 AM   #6
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Re: Rate problem

Quote:
Originally Posted by The Chaz
Quote:
 Originally Posted by daigo Dangit. Maybe I should pursue a degree in something other than mathematics-related 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)
That's no way to talk! Sometimes students first hire me (as a tutor) when they are on their third OR FOURTH try at College Algebra. Of course, I blame the teachers somewhat...

Don't be discouraged!
But it makes me wonder how well I will do in graduate level real analysis or topology, and I think second chances are extremely difficult to come by in a particular field as a PhD candidate as opposed to just "re-trying" at the undergrad level..

February 29th, 2012, 08:59 AM   #7
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Re: Rate problem

Quote:
 Originally Posted by daigo I can do everything except word/application problems ....
Boy...I simply "detest" the use of term "word problem"!

Non-word 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, 10:07 AM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 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, 01:04 AM   #9
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Re: Rate problem

Quote:
 Originally Posted by The Chaz Of course, I blame the teachers somewhat...
I can't help but agree with that.

March 1st, 2012, 01:07 AM   #10
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From: USA

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Re: Rate problem

Quote:
 Originally Posted by daigo Dangit. Maybe I should pursue a degree in something other than mathematics-related 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)
You could always design computer games.

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