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

AAPL wrote: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

OA B

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

AAPL wrote: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

OA B

The respective rates of Paul, Abdul, and Adam are 1/3, 1/4, and 1/5. We can let t = the time during which all three people work together; thus, their 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, the fraction of the job that Adam will complete is (1/5)t/(47/60)t = 60/(47 x 5) = 12/47.

Alternate Solution:

First, let’s determine 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