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

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JubtaGubar
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Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   01 May 2012, 09:41
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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)
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D
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Bunuel
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   02 May 2012, 09:18
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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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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   02 May 2012, 09:03
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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   01 May 2012, 11:59
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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, 12:19
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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, 15:28
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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)


Similar questions to practice:
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, 05:32
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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   27 May 2012, 04:35
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, 23:04
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\(R-rate=\frac{1}{ahrs}\)
\(A-rate=\frac{1}{bhrs}\)

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, 02:25
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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, 11:46
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, 21:16
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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, 17:32
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   03 Dec 2018, 01:48
VeritasKarishma
Can you help me with this problem?

I set up numbers and got this question wrong.
I supposed
Total work is 60 units
Randy produces 3 units / hour
Alvin produces 2 units / hour
Together they produce 5 units / hour
60 / 5 = 12 hours
Randy did 36 units, Alvin did 24 units
The part Randy did not produce is 24 units, so I arrived at 24/60 = 2/5 = 2/(3+2)
What did I do wrong?
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Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   05 Dec 2018, 06:10
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lary301254M7 wrote:
VeritasKarishma
Can you help me with this problem?

I set up numbers and got this question wrong.
I supposed
Total work is 60 units
Randy produces 3 units / hour
Alvin produces 2 units / hour
Together they produce 5 units / hour
60 / 5 = 12 hours
Randy did 36 units, Alvin did 24 units
The part Randy did not produce is 24 units, so I arrived at 24/60 = 2/5 = 2/(3+2)
What did I do wrong?


You did nothing wrong here. But what are a and b here?
a - Time taken by Randy to do the work = 60/3 = 20 hrs
b - Time taken by Alvin to do the work = 60/2 = 30 hrs

When you put a = 20 and b = 30 in option (D), you get 2/5 (which is expected).

P.S. - For a quicker turn around, just drop in a message on my PS Expert thread too
https://gmatclub.com/forum/veritas-prep ... 78042.html
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   05 Dec 2018, 18:20
@E-gmat I tried using your LCM method but doesnt seem to work.

Bunuel can we do this without by number picking ? I tried but kept getting wrong answer.
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   05 Dec 2018, 21:13
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hero_with_1000_faces wrote:
@E-gmat I tried using your LCM method but doesnt seem to work.

Bunuel can we do this without by number picking ? I tried but kept getting wrong answer.


Have you checked THIS POST?
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Re: Randy can rebuild an automobile engine in a hours. Alvin can [#permalink] New post   06 Dec 2018, 04:41
Yes Bunuel,
However, I tried doing this by Number Picking and than taking LCM of the Number:
So, this is How i tried doing:

Randy "a" hours = 3 (assumed) and Alvin "b" hours = 2 (assumed) .

So, work (LCM) = 6, thus Randy does "2 units" in 1 hour and Alvin does "3 units" in 1 hour. So 5 units in 1 hour.

therefore they do 6/5 = 1.2 hours of work
and Alvin only does 3.6 unit of work. "replacing this in correct answer Choice we get"

3/5 = so not matching ? I dont get it, usually this method works like a charm, but here this doesnt seem to work, is it because "Number Picking" doesn't always work ?
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