Working at their respective constant rates, Paul, Abdul and

[BTGmoderatorLU]

Source: Veritas Prep

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

The OA is B

[Jay@ManhattanReview]

Source: Veritas Prep

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

The OA is B

Work done by Paul, Abdul, and Adam alone in one hour = 1/3, 1/4 and 1/5, respectively.

Work done by Paul, Abdul, and Adam together in one hour = 1/3 + 1/4 + 1/5 = 47/60

Fraction of the work will be done by Adam = Part of the work done by Adam / Part of the work done by Adam Paul, Abdul, and Adam together = (1/5) / (47/60) = 12/47

The correct answer: B

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Source: Veritas Prep

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

The OA is B

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

[Scott@TargetTestPrep]

Source: Veritas Prep

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

The OA is B

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 will complete (1/5)t/(47/60)t = 60/(47 x 5) = 12/47 of the job.

Alternate Solution:

First, let's find how much time it takes for the three of them to complete the job. Notice that in 1 hour, Paul, Abdul and Adam can do 1/3, 1/4 and 1/5 of the job, respectively. Thus, with all of them working together,

1/3 + 1/4 + 1/5 = 47/60

of the job gets done in one hour. If 47/60 of the job takes one hour to complete, then the whole job will take 60/47 hours to complete.

Next, we can set up a proportion to determine how much of the job gets done by Adam. Keeping in mind that Adam can do 1/5 of the job in one hour, we set up the proportion: "1/5 of the job is to 1 hour as x of the job is to 60/47 hours"

(1/5)/1 = x/(60/47)

x = (1/5)*(60/47) = 12/47

Answer: B