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Randy can rebuild an automobile engine in a hours. Alvin can

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Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 01 May 2012, 08:41
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Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)
[Reveal] Spoiler: OA
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 01 May 2012, 10:59
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JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
A) ab/(a+b)
B) (a-b)/(a+b)
C) b/(b-a)
D) a/(a+b)
E) b/(a+b)


Let total work completion be denoted as 1.
Randy and Alvin can together complete work in ab/a+b hours.
Randy's 1hr work is 1/a.
Alvin's 1 hr work is 1/b.

Alvin's portion of total work = Alvin's 1hr work /total 1 hr work.
=(1/b)/((a+b)/ab)
=a/(a+b)
That's the portion of work Randy need not do.

D.

Hope that helps.
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 01 May 2012, 11:19
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Rate of Randy - 1/a
Rate of Alvin 1/b

sum of their rates =1/a+1/b=(a+b)/ab

the job that Randy will not have to complete = 1 - (rate of randy/total rate)=
=1- (1/a)/(a+b)/ab=a/(a+b)

d is the answ
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 01 May 2012, 14:28
Expert's post
JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)


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machine-a-can-complete-a-certain-job-in-x-hours-machine-b-126639.html
baker-s-dozen-128782-20.html#p1057508
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 02 May 2012, 04:32
Thank you for explanation, but I still cannot understand what is asked in a question:
which of the following represents the portion of the job that Randy will not have to complete

could you please explain the task clearer?
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 02 May 2012, 08:03
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JubtaGubar wrote:
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)


Randy can do the job in a hrs, Alvin can do the job in b hrs.

When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.

Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)

So Randy does b/(a+b) of the work and Alvin does a/(a+b) of the work.

Answer (D).
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 02 May 2012, 08:18
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JubtaGubar wrote:
Thank you for explanation, but I still cannot understand what is asked in a question:
which of the following represents the portion of the job that Randy will not have to complete

could you please explain the task clearer?


Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
A. ab/(a+b)
B. (a-b)/(a+b)
C. b/(b-a)
D. a/(a+b)
E. b/(a+b)

The rate of Randy is \(\frac{1}{a}\) job/hour;
The rate of Alvin is \(\frac{1}{b}\) job/hour;

Their combined rate is \(\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}\), so working together they will complete the job in \(\frac{ab}{a+b}\) hours.

Now, in \(\frac{ab}{a+b}\) hours Alvin will complete \(\frac{1}{b}*\frac{ab}{a+b}=\frac{a}{a+b}\) part of the job (rate*time=job) and this will be the part which Randy will not have to complete.

Answer: D.
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Kaplan free test PS [#permalink] New post 26 May 2012, 21:08
Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

1. ab/(a+b)
2.(a-b)/(a+b)
3.b/(b-a)
4. a/(a+b)
5.b/(a+b)
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Re: Kaplan free test PS [#permalink] New post 26 May 2012, 21:09
ok so Kaplan solved it by substituting numbers. But can anyone explain how algebraically we can solve this? I am thoroughly perplexed!
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Re: Kaplan free test PS [#permalink] New post 27 May 2012, 02:17
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 27 May 2012, 03:35
thanks Bunuel. its clear now!
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 15 Nov 2012, 22:04
\(R-rate=\frac{1}{ahrs}\)
\(A-rate=\frac{1}{bhrs}\)

Rate of working together
\(\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}\)

Time=reciprocal of rate together
\(t=\frac{ab}{a+b}\)

Work done by Alvin
\(W=\frac{1}{b}(ab/a+b)=\frac{a}{a+B}\)

Answer:D
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 28 Sep 2013, 01:25
a=2
b=3

1/a + 1/b = 5/6 Rate

Rate * Time = Work
5/6 * Time = 1

Time = 6/5

Hence both of them work for 6/5 hours

Work done by b in 6/5 hours is

1/3 * 6/5 = 2/5

Check the options for work done = 2/5 for above given values of a and b
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 21 Nov 2013, 10:46
I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do.
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 21 Nov 2013, 20:16
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AccipiterQ wrote:
I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do.


When the question asks you: which of the following represents the portion of the job that Randy will not have to complete?
it is just another way of saying: which of the following represents the portion of the job that Alvin will do?

If I and you are working on something, you will not have to do the work that I am completing. So look at it from Alvin's perspective.

Work done by Alvin = (Rate of Alvin)*(Time taken to complete the job together) = (1/b)*(ab/(a+b)) = a/(a+b)
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 22 Nov 2013, 16:32
VeritasPrepKarishma wrote:
AccipiterQ wrote:
I solved by plugging smart numbers. I don't get it conceptually though, how can the amount of work someone DOESN'T have to do be their time to do the job, divided by the total time each would take to do the job. Seems like that would give you the amount of time it took Randy to do the work, not the portion he DIDN'T have to do.


When the question asks you: which of the following represents the portion of the job that Randy will not have to complete?
it is just another way of saying: which of the following represents the portion of the job that Alvin will do?

If I and you are working on something, you will not have to do the work that I am completing. So look at it from Alvin's perspective.

Work done by Alvin = (Rate of Alvin)*(Time taken to complete the job together) = (1/b)*(ab/(a+b)) = a/(a+b)



ah, when you word it that way it makes perfect sense!
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post 08 Dec 2014, 08:14
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Re: Randy can rebuild an automobile engine in a hours. Alvin can   [#permalink] 08 Dec 2014, 08:14
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