My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 29th, 2012, 05:58 AM   #1
Senior Member
 
Joined: Jan 2010

Posts: 205
Thanks: 0

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
daigo is offline  
 
February 29th, 2012, 06:24 AM   #2
Global Moderator
 
The Chaz's Avatar
 
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.
The Chaz is offline  
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
superconduct is offline  
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 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)
daigo is offline  
February 29th, 2012, 07:23 AM   #5
Global Moderator
 
The Chaz's Avatar
 
Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

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!
The Chaz is offline  
February 29th, 2012, 07:56 AM   #6
Senior Member
 
Joined: Jan 2010

Posts: 205
Thanks: 0

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..
daigo is offline  
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:
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.
Denis is offline  
February 29th, 2012, 09:07 AM   #8
Senior Member
 
MarkFL's Avatar
 
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.
MarkFL is offline  
March 1st, 2012, 12:04 AM   #9
Senior Member
 
Joined: Apr 2011
From: USA

Posts: 782
Thanks: 1

Re: Rate problem

Quote:
Originally Posted by The Chaz
Of course, I blame the teachers somewhat...
I can't help but agree with that.
Erimess is offline  
March 1st, 2012, 12:07 AM   #10
Senior Member
 
Joined: Apr 2011
From: USA

Posts: 782
Thanks: 1

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.
Erimess is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
problem, rate



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Derivative/rate problem daigo Calculus 4 July 14th, 2012 09:36 AM
Rate problem daigo Calculus 4 July 10th, 2012 11:11 AM
Please help with this rate differentiation problem! I've tri rockit_hiro Calculus 7 October 27th, 2011 04:29 PM
a man can run...(rate problem) warqzaka Algebra 6 July 21st, 2011 04:23 PM
work rate problem e81 Algebra 2 May 15th, 2011 10:54 AM





Copyright © 2019 My Math Forum. All rights reserved.