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Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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23 Sep 2011, 00:35
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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? (A) 1/4 (B) 12/47 (C) 1/3 (D) 5/12 (E) 20/47 Innovative Solutions will be highly Appreciated.
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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23 Sep 2011, 00:56
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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 >( 60/47 *12)/60 =12/47 Answer B



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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23 Sep 2011, 01:01
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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.



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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23 Sep 2011, 01:04
Work is measured in job per unit time. Let j be job Rate of work done by Paul= J/3= 0.33J Abdul= J/4= 0.25J Adam=J/5=0.2J Relative rate w.r.t Adam Paul= 0.33/0.2=1.65 Abdul=0.25/2=1.25 Adam=1 Hence relative proportion of work done= 1.65:1.25:1 Adam's share= 1/(1.65+1.25+1)=1/3.9 Closest option is 12/47 B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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23 Sep 2011, 01:10
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.



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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25 Sep 2011, 09:29
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In this approach we consider the work as some unit of work = 1 PaulAbdulAdam Rate1/31/41/5 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.



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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25 Sep 2011, 09:50
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
Answer B.



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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, 02:37
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 Adams contribution will be Total work done X Adams's rate of work 60/47X1/5=12/47



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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27 Sep 2016, 01:16
[1/5]/[1/3+1/4+1/5] = 60 / (5*47) = 12/47 is the answer



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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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16 Aug 2017, 07:46
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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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