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Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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23 Sep 2011, 01:35

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Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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23 Sep 2011, 01:56

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GMATPASSION wrote:

Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4 (B) 12/47 (C) 1/3 (D) 5/12 (E) 20/47

Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.

adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work

Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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25 Sep 2011, 10:29

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In this approach we consider the work as some unit of work = 1

-------Paul----Abdul----Adam

Rate---1/3-----1/4------1/5

when they all work together their combined rate = 1/3+1/4+1/5 = 47/60

time taken by them to finish to unit work = 60/47 hours

work done by adam in 60/47 hours = (60/47)*(1/5) = 12/47

fraction of work done by adam = adam's work / total work = (12/47) / 1 = 12/47

So coming back to your question its 1 unit of work here. thats why the total work they can do= 1. you can consider the work done as some 'w' still the answer would be same.

Answer is B.

GMATPASSION wrote:

vishal4584 wrote:

We can solve the problem just by calculating the work done in 1 hr.

Work done by adam in 1 hr is 1/5. total work done by all three in 1 hr is (1/3 + 1/4 +1/5) = 47/60

so, fraction of work done by Adam = (1/5)/(47/60) = 12/47.

Option B.

Your Solution Here seems to be good. But I would like To clarify Some silly doubts:

If all three work together to finish the work, what fraction of the work will be done by Adam-- Question asks us to find :

Ratio of work done by adam/ Work Done by all three .

But you have based ur calculations on only 1 hour. Why is that? Infact, all three take longer than 1 hour to finish the work.

Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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25 Sep 2011, 10:50

Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4 (B) 12/47 (C) 1/3 (D) 5/12 (E) 20/47

Step 1: find the individual rates by finding the inverse of the times - Paul: 1/3, Abdul: 1/4, Adam: 1/5 Step 2: add the rates - 1/3 + 1/4 + 1/5 = 47/60 Step 3: the inverse of the combined rate above tells you the time. i.e. takes 60/47 hours to finish the job together Step 4: apply the 60/47 hours to Adam's rate to find his share of work - W = 1/5*60/47 = 12/47

Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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20 Mar 2016, 03:37

GMATPASSION wrote:

Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4 (B) 12/47 (C) 1/3 (D) 5/12 (E) 20/47

Innovative Solutions will be highly Appreciated.

Rate of work done Paul 1/3 Abdul 1/4 Adam 1/5

Total rate of work 1/3+1/4+1/5=47/60

Total work done is inverse of total rate of work=60/47

Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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16 Aug 2017, 08:46

Say there are 60 units of work to be done.So

Paul takes 3 hrs => in 1 hr he completes 20 units of work Abdul takes 4 hrs => in 1 hr he completes 15 units of work Adam takes 5 hrs => in 1 hr he completes 12 units of work

In 1 hour all together can complete 47 units of work. Hence time taken to complete 60 units of work is 60/47 hours.

Now in 60/47 hours Adam completes (12*60)/47 units of work. Hence his contribution would be (12*60)/(47*60) which is 12/47.
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