BTGmoderatorLU wrote: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
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