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Working at their respective constant rates, Paul, Abdul and Adam alone

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

(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
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B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   23 Sep 2011, 02:01
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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] New post   09 Aug 2019, 09:22
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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

Innovative Solutions will be highly Appreciated.


One approach is to assign a "nice" value to the entire job. That is, a value that works well with the given information (3, 4, and 5 hours).
The least common multiple of 3, 4 and 5 is 60.
So, let's say the ENTIRE job consists of making 60 widgets.

If Paul can complete the job (make 60 widgets) in 3 hours, then his RATE of work = 20 widgets PER HOUR
If Abdul can make 60 widgets in 4 hours, then his RATE of work = 15 widgets PER HOUR
If Adam can make 60 widgets in 5 hours, then his RATE of work = 12 widgets PER HOUR
So, if they work TOGETHER, their combined RATE = 20 + 15 + 12 = 47 widgets PER HOUR

So, for every HOUR that passes, the GROUP can make 47 widgets
We also know that, for every HOUR that passes, the Adam can made 12 widgets (since his RATE of work = 12 widgets PER HOUR)

This means that, when the 3 people work together, Adam makes 12/47 of the widgets

Answer: B

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

>( 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] New post   23 Sep 2011, 02:04
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] New post   23 Sep 2011, 02:10
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] New post   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.
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   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

Answer B.
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   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

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] New post   27 Sep 2016, 02:16
[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] New post   16 Aug 2017, 08:46
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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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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   15 Mar 2019, 07:42
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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

Innovative Solutions will be highly Appreciated.


We can let t = the time during which all three people work together; thus, the combined work is:

(1/3)t + (1/4)t + (1/5)t = (20/60)t + (15/60)t + (12/60)t = (47/60)t

Thus, Adam completed (1/5)t/[(47/60)t] = 60/(47 x 5) = 12/47 of the job.

Answer: B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   09 Jun 2019, 07:38
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.


Solution



Name,R,T,W
Paul: 1/3, 3
Abdul: 1/4, 4
Adam: 1/5, 5


Method 1: Fractions


Total Rate = 1/3 + 1/4 + 1/5 = (20+15+12)/60 = 47/60
Fraction of work done by Adam: (60/47) * (1/5) = 12/47


Method 2: LCM Method


Rate for Paul: Abdul: Adam: Total
20:15:12: 47
Fraction of work done by Adam: 12/27
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   18 Aug 2019, 10:02
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.


combined rate ; 1/3+1/4+1/5 ; 47 /60
so time 60/47 and rate of Adam ; 1/5 so work done ; 60/47 * 1/5 ; 12/47
IMO B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   18 Aug 2019, 10:19
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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

Innovative Solutions will be highly Appreciated.


Given: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively.

Asked: If all three work together to finish the work, what fraction of the work will be done by Adam?

Ratio of work done by Paul: Abdul: Adam = 1/3: 1/4:1/5 = 20:15:12

Fraction of the work done by Adam \(= \frac{12}{(20+15+12)} = \frac{12}{47}\)

IMO B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   16 Oct 2020, 13:10
Paul's rate: 1/3
Abdul's rate: 1/4
Adam's rate: 1/5

Rates are additive; Paul + Abdul + Adam = 47/60

Adam's rate = 12/60

12/47. Answer is B.
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   30 Nov 2021, 20:20
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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?

Assume that total work = LCM (3,4,5) = 60 units

Per hour Work:

Amount of work done by Paul in 1 hr = 60/3 = 20 units
Amount of work done by Abdul in 1 hr = 60/4 = 15 units
Amount of work done by Adam in 1 hr = 60/5 = 12 units

Paul, Abdul and Adam will do 20 + 15 + 12 = 47 units work in 1 hr if they all work together.

Then the fraction of work done by Adam = 12/47

Option B is the answer.

Thanks,
Clifin J Francis,
GMAT SME
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink] New post   17 Nov 2023, 23:26
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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

Innovative Solutions will be highly Appreciated.


Time taken by Paul:Abdul:Adam is in the ratio 3:4:5.
Their rate of work ratio will be the inverse of this i.e. 1/3 : 1/4 : 1/5
We can multiply each term by 60 to get simple integer ratio i.e. 20 : 15 : 12

Hence, when Paul does 20 units of work, in the same time, Abdul does 15 units and Adam does 12 units. Hence Adam does 12 units in every total 47 units of work they do.
So Adam does 12/47 of the work

Answer (B)

Check this video on how to use ratios for work-rate: https://youtu.be/88NFTttkJmA
and check out these posts: https://anaprep.com/arithmetic-applying ... -concepts/
https://anaprep.com/arithmetic-work-rat ... s-and-all/
https://anaprep.com/arithmetic-avoiding ... work-rate/
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]
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