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Algebra

by heshamelaziry » Mon Oct 19, 2009 8:45 pm
Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?

(1) x-y/x+y

(2) x/y-x

(3) x+y/xy

(4) y/x-y

(5) y/x+y

OA 5
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Re: Algebra

by papgust » Mon Oct 19, 2009 10:54 pm
heshamelaziry wrote:which of the following represents the fraction of the job that B will not have to complete?
Is it "B will have to complete" in the qn? In that case, E makes sense
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Re: Algebra

by heshamelaziry » Mon Oct 19, 2009 11:04 pm
papgust wrote:
heshamelaziry wrote:which of the following represents the fraction of the job that B will not have to complete?
Is it "B will have to complete" in the qn? In that case, E makes sense
Please provide explanation.
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by papgust » Tue Oct 20, 2009 1:03 am
I guess i misunderstood the question. Agree that the question is worded fine.

A takes x hrs
B takes y hrs

Together, (x+y)/xy job

Qn says fraction of a job B will NOT have to complete - This means that it refers to job done by A.

Therefore, fraction of job done by A will be (1/x)/[(x+y)/xy] ==> (1/x)*(xy/x+y)

Therefore, answer is y/x+y. Hope my approach is fine.
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by heshamelaziry » Tue Oct 20, 2009 8:30 am
papgust wrote:I guess i misunderstood the question. Agree that the question is worded fine.

A takes x hrs
B takes y hrs

Together, (x+y)/xy job

Qn says fraction of a job B will NOT have to complete - This means that it refers to job done by A.

Therefore, fraction of job done by A will be (1/x)/[(x+y)/xy] ==> (1/x)*(xy/x+y)

Therefore, answer is y/x+y. Hope my approach is fine.
I hope you can be patient with me :) . If B does y then seems to me that B fraction of the job is y/y+x so B fraction of the job that it does NOT do is A part of the job that it does, then it should be x/x+y !!!!

I don't know what I am missing !!!!
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by regor60 » Tue Oct 20, 2009 9:04 am
heshamelaziry wrote: I hope you can be patient with me :) . If B does y then seems to me that B fraction of the job is y/y+x so B fraction of the job that it does NOT do is A part of the job that it does, then it should be x/x+y !!!!

I don't know what I am missing !!!!
Fraction that B does is not as you describe. Fraction of JOB is like Distance =RatexTime. The rate is 1/x and 1/y. Distance = job, or 1. Therefore, the portion completed by B in a unit of time is 1/y, likewise the portion done by A is 1/x. The fraction of the whole job done by B is 1/y/(1/x)+(1/y), or x/(x+y)
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by Ludacrispat26 » Tue Oct 20, 2009 1:05 pm
Bah, don't know if this is right but I just did it by:

X= 1 hour
Y= 1 hour

It will take them 1/2 hour to complete it together, so Y only needs to do half as much work as normal.

I then just plugged in until E where y/(x+y) was 1/2, which got me the answer.

However, I'm sure an expert can tell you how to get it without plugging in much faster
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by heshamelaziry » Tue Oct 20, 2009 7:03 pm
Ludacrispat26 wrote:Bah, don't know if this is right but I just did it by:

X= 1 hour
Y= 1 hour

It will take them 1/2 hour to complete it together, so Y only needs to do half as much work as normal.

I then just plugged in until E where y/(x+y) was 1/2, which got me the answer.

However, I'm sure an expert can tell you how to get it without plugging in much faster
This turned out to be simple work problem; if there were numbers, it would have been clear. I saw this question with numbers, but solved differently, and so got confused. Also, i got tricked by the part that machine B does not do.

say A = 2 , B = 3----> 1/2 + 1/3 = 5/6----> take reciprocal of 5/6 to get time taken if both work together.
Now, the fraction of the job that machine B does not do is that fraction of the job that machine A does. So, (1/2) / (5/6) = something
:)
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by papgust » Tue Oct 20, 2009 9:20 pm
heshamelaziry wrote:
papgust wrote:I guess i misunderstood the question. Agree that the question is worded fine.

A takes x hrs
B takes y hrs

Together, (x+y)/xy job

Qn says fraction of a job B will NOT have to complete - This means that it refers to job done by A.

Therefore, fraction of job done by A will be (1/x)/[(x+y)/xy] ==> (1/x)*(xy/x+y)

Therefore, answer is y/x+y. Hope my approach is fine.
I hope you can be patient with me :) . If B does y then seems to me that B fraction of the job is y/y+x so B fraction of the job that it does NOT do is A part of the job that it does, then it should be x/x+y !!!!

I don't know what I am missing !!!!
As i mentioned this will be the formula

Fraction of job done by A will be (1/x)/[(x+y)/xy] ==> (1/x)*(xy/x+y)

x gets cancelled out for the job done by A resulting in y/x+y
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