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A qualified worker digs a well in 5 hours

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A qualified worker digs a well in 5 hours

by gmatdriller » Sat Jan 10, 2015 4:11 am
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

OA is C

My analysis:
The Qualified worker takes 5hrs;

2 Appr work at 3/4 as fast as the Qualified worker;
I think both Appr would take 5/(3/4)hrs right?

e.g if Q takes 5hrs and I say, W works twice as fast as the rate of Q.
Then W takes 5/2 = 2.5hrs?

Pls correct my analysis.

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by GMATGuruNY » Sat Jan 10, 2015 4:25 am
gmatdriller 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 well = 100 units.
Since the qualified worker takes 5 hours to dig the well, the qualified worker's rate = w/t = 100/5 = 20 units per hour.
Since each apprentice works 3/4 as fast, the rate for each apprentice = (3/4)(20) = 15 units per hour.
Since each trainee works 1/5 as fast, the rate for each trainee = (1/5)(20) = 4 units per hour.
Combined rate for the qualified worker, 2 apprentices and 2 trainees = 20 + 2*15 + 2*4 = 58 units per hour.
Time for all 5 workers to dig the well = w/r = 100/58 ≈ 100/60 = 5/3 hours = 1 hour, 40 minutes.

The correct answer is C.
Last edited by GMATGuruNY on Mon Jan 12, 2015 4:10 am, edited 1 time in total.
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by gmatdriller » Sat Jan 10, 2015 4:51 am
GmatGuru, thanks for the explanations.

2 issues:
(i) what is wrong with my analysis; I need to deduce time for the invited pple
(ii) The question did not say the rate is for EACH of the 2 pple invited.
It says BOTH work 3/4 as fast as the qualified worker
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by Brent@GMATPrepNow » Sat Jan 10, 2015 10:10 am
gmatdriller wrote: 2 Appr work at 3/4 as fast as the Qualified worker;
I think both Appr would take 5/(3/4)hrs right?
This is incorrect.
Note that 5/(3/4) is less than 5.
This would mean that each apprentice works faster than the qualified worker, and that is not the case.
Each apprentice will take 4/3 as long to dig the well.
So, each apprentice will take (5)(4/3) hours

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by Brent@GMATPrepNow » Sat Jan 10, 2015 10:28 am
gmatdriller 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 prefer the approach Mitch used, however here's another solution:

For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let's use these rules to solve the question. . . .

A qualified worker digs a well in 5 hours
Applying Rule #1, we know that in ONE HOUR, the worker can complete 1/5 of the job.
ASIDE: This means the worker's rate = 1/5 of the job per hour.

Each apprentice works 3/4 as fast
So, in ONE HOUR, an apprentice can complete (3/4)(1/5) of the job.
In other words, each apprentice can complete 3/20 of the job in 1 hour.

Each trainee works 1/5 as fast
So, in ONE HOUR, a trainee can complete (1/5)(1/5) of the job.
In other words, each trainee can complete 1/25 of the job in 1 hour.

So, in ONE HOUR, the total work completed = 1/5 + 3/20 + 3/20 + 1/25 + 1/25
Add fractions with common denominator of 100 to get: 20/100 + 15/100 + 15/100 + 4/100 + 4/100
Combine to get: 58/100
In other words, in ONE HOUR, the team can complete 58/100 of the job.

Applying Rule #2, the time to complete the entire job = 100/58 hours.
100/58 = 1 42/58

IMPORTANT: 42/60 = 42 minutes. So, 42/58 will be a little bit MORE than 42 minutes.
Answer choice [spoiler] C (with 44 minutes)[/spoiler] is the best option.

Answer: C

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by Brent@GMATPrepNow » Sat Jan 10, 2015 10:37 am
gmatdriller 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
Here are 2 nitpicky reasons why this question is not up to GMAT standards:

1) The question asks, How much time does the team need to finish the job?
Answer choices like 1:24 are ambiguous. This could mean 1 minute and 24 seconds.
The GMAT's test-makers would provide the answer choices as 1 hour 24 minutes, etc.

2) The correct answer of 100/58 hours does not match any of the answer choices. In fact, 100/58 hours is closer to 1 hour 43 minutes than it is to 1 hour 44 minutes (answer choice C). In these instances, the question would include wording to the effect that we're looking for an APPROXIMATE answer.

Cheers,
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