Sumukh19 wrote:
Pat takes 4 hours to complete a job, Quinn takes 6 hours and Rob takes 8 hours to complete the same job when they work alone. If the three people work together to complete the same job, approximately what percentage of the total work is done by Pat?
A. 42%
B. 46%
C. 50%
D. 54%
E. 60%
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When it comes to Work questions in which workers complete a
job, it's often quickest to assign a nice value to the job.
In this case we want a value that works well with the three given numbers, 4, 6 and 8
The least common multiple of 4, 6 and 8 is
24So, let's say the entire job consists of making
24 widgets.
So, the given information is actually telling us the following....
Pat takes 4 hours to make
24 widgets, which means Pat's RATE = 6 widgets per hour
Quinn takes 6 hours to make
24 widgets, which means Quinn's RATE = 4 widgets per hour
Rob takes 8 hours to make
24 widgets, which means Rob's RATE = 3 widgets per hour
Their COMBINED RATE = 6 + 4 + 3 =
13 widgets per hour.
So, in one hour, the three workers make a total of
13 widgets
We also know that, in one hour, Pat makes
6 widgets
(and Quinn makes 4 widgets, and Rob makes 3 widgets).
In other words, for every hour worked, Pat makes
6/
13 of all the widgets made.
6/
13 ≈ 46%
Answer: B
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