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

Question

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)

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

Bunuel · Accepted Answer

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.

KarishmaB · Answer

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).

NightFury · Answer

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.

LalaB · Answer

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

Bunuel · Answer

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

JubtaGubar · Answer

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?

vibhav · Answer

thanks Bunuel. its clear now!

mbaiseasy · Answer

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

TGC · Answer

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

AccipiterQ · Answer

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.

KarishmaB · Answer

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)

AccipiterQ · Answer

ah, when you word it that way it makes perfect sense!

lary301254M7 · Answer

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?

KarishmaB · Answer

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

hero_with_1000_faces · Answer

@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.

Bunuel · Answer

Have you checked  THIS POST ?

hero_with_1000_faces · Answer

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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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

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