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A qualified worker digs a well in 5 hours. He invites 2 appr

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A qualified worker digs a well in 5 hours. He invites 2 appr

by hazelnut01 » Wed Mar 15, 2017 6:20 pm
A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working 3/4 as fast as the qualified worker and 2 trainees each working 1/5 as fast as the qualified worker. If the five-person team digs the same well, approximately how much time does the team need to finish the job?

(A) 1 hour 24 minutes
(B) 1 hour 34 minutes
(C) 1 hour 44 minutes
(D) 1 hour 54 minutes
(E) 2 hours 14 minutes
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by Jay@ManhattanReview » Wed Mar 15, 2017 8:01 pm
ziyuenlau wrote:A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working 3/4 as fast as the qualified worker and 2 trainees each working 1/5 as fast as the qualified worker. If the five-person team digs the same well, approximately how much time does the team need to finish the job?

(A) 1 hour 24 minutes
(B) 1 hour 34 minutes
(C) 1 hour 44 minutes
(D) 1 hour 54 minutes
(E) 2 hours 14 minutes
Hi ziyuenlau,

This is a typical Time and Work question on calculating the combined rate of three persons.

We have:

Rate of the qualified worker = 1/5

Rate of two apprentices = 2∗(1/5)∗(3/4) = 3/10

Rate of two trainees = 2∗(1/5)∗(1/5) = 2/25

Combined rate of all five people = (1/5) + (3/10) + (2/25) = 29/50 part of work per hour

Time required to dig the Well = 50/29 hours = 1 hour (21/29)*60 minutes > 1 hour (21/30)*60 minutes = 1 hour 42 minutes

Since the correct answer must be a little more than 1 hour 42 minutes, the correct answer would be 1 hour 44 minutes.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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by [email protected] » Wed Mar 15, 2017 10:39 pm
Hi ziyuenlau,

These types of 'Work' questions can be solved in a couple of different ways (depending on how you want to 'organize' the rate information). It can often help to think in terms of the number of worker-hours required to complete the job.

The Qualified Worker takes 5 hours to complete a job, so the job requires 5 Worker-hours of effort to be finished.

The Qualified Worker can complete 1 Worker-hour per hour.
Each of the two apprentices can complete 3/4 of a Worker-hour per hour.
Each of the two trainees can complete 1/5 of a Worker-hour per hour.

Total = 1 + 2(3/4) + 2(1/5) = 1 + 1.5 + .4 = 2.9 Worker-hours completed per hour by this group.

Since the job requires 5 Worker-hours of effort, the total time will be...

5/2.9 hours =
50/29 hours =
1 21/29 hours

21/29 is a little more than 2/3 (since 20/30 = 2/3). Thus, we're looking for an answer that is a little more than 1 2/3 hours. There's only one answer that matches....

Final Answer: C

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