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

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Intern
Joined: 17 Oct 2015
Posts: 17
Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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09 Jan 2016, 10:15

We need to do this because of the formula: R x T = J ?

So:
(29/50) x t = 1
t = 1 / (29/50)
t = 50/29

Thats it?

Regards.

chetan2u wrote:
mestrec wrote:
I did just like you and have the same doubt.. If someone could help.

undecidedonmba wrote:
A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A) 1:24
B) 1:34
C) 1:44
D) 1:54
E) 2:14

I started with the original rate for the worker as 1/5.

Each apprentice would have a rate (1/5)*(3/4) = 3/20

Each trainee would have a rate (1/5) * (1/5) = 1/25

Combining all of it together 1/5 + 3/20 + 3/20 + 1/25 + 1/25 = 58/100 per hour

After one hour, the remaining work to be done is 42/100

Is it possible to use this approach to solve the problem?

Hi,
the method is perfect, it only misses out on last step..

what you are getting 58/100 is one hour work..
so the time required will be reciprocal of this=100/58= 1 42/58, which approx equal to 1:44..
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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09 Jan 2016, 10:16
1
mestrec wrote:

We need to do this because of the formula: R x T = J ?

So:
(29/50) x t = 1
t = 1 / (29/50)
t = 50/29

Thats it?

Regards.

Yes, you are correct.
Math Expert
Joined: 02 Aug 2009
Posts: 7984
Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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09 Jan 2016, 10:30
1
mestrec wrote:

We need to do this because of the formula: R x T = J ?

So:
(29/50) x t = 1
t = 1 / (29/50)
t = 50/29

Thats it?

Regards.

chetan2u wrote:

Hi,
the method is perfect, it only misses out on last step..

what you are getting 58/100 is one hour work..
so the time required will be reciprocal of this=100/58= 1 42/58, which approx equal to 1:44..

Yes, you are absolutely correct with your observation..
Moreover most of the Qs related to this aspect follow these steps..
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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23 Jan 2016, 22:30
cicerone wrote:
I have another way.

A can do a work in 5 hours.

Now 2 persons whose efficiency is 3/4 of A joins him.
ie 1 person whose efficiency is 2x3/4 ie 3/2 times of A joins him.

Again 2 persons whose efficiency is 1/5 of A joins him.
ie 1 person whose efficiency is 2x1/5 ie 2/5 times of A joins him.

So finally the people involved in the work is
A+ 3/2(A) + 2/5(A)
ie 29/10 (A)

Since A alone takes 5 hours
29/10 (A) will take 10/29 x 5 i.e 50 /29 hours

IMO

This looks to be a better approach among all...

But will i be able to apply the same in any of the work related problems?

Thanks,
A
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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24 Jan 2016, 02:27
Hermione wrote:
A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24
B. 1:34
C. 1:44
D. 1:54
E. 2:14

Let the qualified worked do 20 units/hr
=> well = 100 units
also, apprentices = 3/4*20 = 15 units/hr
and trainees = 1/5*20 = 4 units/hr
hence, team = (20 + 15*2 + 4*2) = 58 units/hr
we need to get the time of doing 100 units if 58 units are done in 1 hr.
=> 60*100/58 = 103.4 minutes or ~1 hr 44 mins (option C)
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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23 Jun 2016, 11:57
Guys can you edit the answer choices to x hours y minutes please? I was getting 100/58 and then the correct answer says 1/44 i mean thats what it reads... might be confusing to some folks!
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Joined: 07 Dec 2014
Posts: 1224
Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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23 Jun 2016, 14:43
50/29*60=103.45 minutes, or 1:43
why are we rounding it up to 1:44?
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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15 Jan 2018, 13:12
Hi All,

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....

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Re: A qualified worker digs a well in 5 hours. He invites 2 appr  [#permalink]

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11 Mar 2019, 11:10
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Re: A qualified worker digs a well in 5 hours. He invites 2 appr   [#permalink] 11 Mar 2019, 11:10

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