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Combining work rates (other ways to solve these problems?)

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Intern
Joined: 22 Jan 2005
Posts: 15
Combining work rates (other ways to solve these problems?) [#permalink]

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22 Jan 2005, 11:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How do you solve the fractional expression in the first problem?
What other ways are there to solve this type of problem?

Q: If Tom can do a job in 10 hours and Tom and Mary can do the job in 6 hours working at their respective rates, how long will it take Mary to do the job by herself.

I know of two possible ways to solve this.

(1) Using the (X*Y)/(X+Y) formula I came up with:

(10*M)/(10+M) = 6

Where T=X=10 and Y=M. And because my math skills are rusty I don't know where to go from here. Am I cross multiplying the fractional expression?

(2) Using the Princeton method of pie charts:

Tom = w=120
r=12/hr | t=10hrs

Tom and Mary = w=120
r=10 + M? | t=6hrs

Mary = w=120
r= 10/hr | t= 12hrs

I got the question right after plugging in any Work value that is a multiple of 6 and 10; 60, 120, etc.
Director
Joined: 19 Nov 2004
Posts: 556
Location: SF Bay Area, USA

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22 Jan 2005, 13:39
Rate problems can be tackled easily, if you follow a method.
A simple way to do Rate problems is to use the following formula:

X1/T1 + X2/T2 = J

X1= Time spent together by A
X2 = Time spent together by B
T1 = Time spent alone by A
T2 = Time spent alond by B
J= Fraction of job

Here, X1 =6, X2= 6, T1=10, T2 = unknown, J= 1 (full job)
=> T2 = 15
(This problem could be solved in about 30 second with this method).
This formula can be used for almost all rate problems, including the one that involves many people once you think through the problem and obtain the correct parameters to plug it into the above equation. In GMAT this will help in terms of time!

See another rate problem that is solved easily using this formula at http://www.gmatclub.com/phpbb/viewtopic.php?t=13304
Director
Joined: 07 Jun 2004
Posts: 612
Location: PA

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22 Jan 2005, 13:46
my advice to u is work leess on the formula undrstand the concept of rate and work that will help u and tackle complicated problmes . cuz GMAT Will not give u straight forward problomes where u can plug numbers in a formula

work on fundamentals it may take time but it will stick in your brain!!

thts my opinion
SVP
Joined: 03 Jan 2005
Posts: 2233

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22 Jan 2005, 22:30
Let say Tom's working rate is t and Mary's working rate is m.

10t=6(t+m)
4t=6m
=>10t=15m

In other words, the work that Tom can finish in 10 hours, Mary will need 15 hours to finish it.

It's quite similar to distance problem, actually.
Director
Joined: 27 Dec 2004
Posts: 897

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07 Feb 2005, 10:09
HongHu wrote:
Let say Tom's working rate is t and Mary's working rate is m.

10t=6(t+m)
4t=6m
=>10t=15m

In other words, the work that Tom can finish in 10 hours, Mary will need 15 hours to finish it.

It's quite similar to distance problem, actually.

Here is another approach:

Tom can do a job in 10 hours means he doesn 1/10 of the job in an hour

Tom and Mary can do the same job in 6 hours means they both can get 1/6 of the job done in an hour.

To find Maryâ€™s rate (M), then the sum of their rate per hour = their rate combined per hour.

1/10 + 1/M = 1/6.
1/M = 4/60 (note that this is the time it takes marry per hour)
Take the reciprocal of this fraction and you will get the time it takes marry to complete the same job alone = 60 / 4 = 15 hours.

I hope that helps.
Intern
Joined: 20 Dec 2004
Posts: 14

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25 Mar 2005, 22:09
Nocilis, could you give an example using your method of solving?
Intern
Joined: 25 Feb 2005
Posts: 42

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26 Mar 2005, 00:32
1/T + 1/M = 1/6

1/10 + 1/M = 1/6

1/M = 1/6-1/10
1/M = 4/60 = 1/12

M = 12 hr
Intern
Joined: 25 Feb 2005
Posts: 42

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26 Mar 2005, 00:35
scorer wrote:
1/T + 1/M = 1/6

1/10 + 1/M = 1/6

1/M = 1/6-1/10
1/M = 4/60 = 1/12

M = 12 hr

oops! i mean M=15 hr.
Intern
Joined: 14 Aug 2003
Posts: 7
Location: Texas

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26 Mar 2005, 08:39
HEllo HH, I am trying to learn all the different methods to solve this, but I missed a step in your solution.

How did you go from: 4t=6m to 10t=15m
ThanksTP
Manager
Joined: 17 Dec 2004
Posts: 71

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27 Mar 2005, 22:51
texaspunk wrote:
HEllo HH, I am trying to learn all the different methods to solve this, but I missed a step in your solution.

How did you go from: 4t=6m to 10t=15m
ThanksTP

10t=6(t+m)
4t=6m
t=1.5m

Here, you get the ratio of Tom's work to Mary's work. Knowing that Tom takes 10 hours, you plug that in to the ratio and get 15 for Mary.

I would probably go about it like Folaa3 does... I usually figure out how much of a job each can do in an hour...
SVP
Joined: 03 Jan 2005
Posts: 2233

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28 Mar 2005, 09:39
halahpeno is right. Though I would try to avoid fractions and/or decimals in the test to save time. So what I'd do is this:

4t=6m
2t=3m (divided both sides by 2)
10t=15m (multiply both sides by 5)

28 Mar 2005, 09:39
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