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Pat takes 4 hours to complete a work, Quinn takes 6 hours an
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11 Jan 2022, 03:29
11 Jan 2022, 03:29
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Question Stats:
75% (02:00) correct
25% (01:56) wrong based on 16 sessions
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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%
Posted from my mobile device
A. 42%
B. 46%
C. 50%
D. 54%
E. 60%
Posted from my mobile device
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Pat takes 4 hours to complete a work, Quinn takes 6 hours an
[#permalink]
11 Jan 2022, 07:13
11 Jan 2022, 07:13
2
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%
Posted from my mobile device
A. 42%
B. 46%
C. 50%
D. 54%
E. 60%
Posted from my mobile device
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 24
So, 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
Re: Pat takes 4 hours to complete a work, Quinn takes 6 hours an
[#permalink]
11 Jan 2022, 07:58
11 Jan 2022, 07:58
I was a little bit confused in the final step of the problem. Thanks a lot for the explanation.
Posted from my mobile device
Posted from my mobile device
