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# Angela, Bernie, and Colleen can complete a job, all working together,

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Math Expert
Joined: 02 Sep 2009
Posts: 65785
Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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13 Jul 2015, 23:56
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Difficulty:

5% (low)

Question Stats:

90% (01:04) correct 10% (01:37) wrong based on 112 sessions

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Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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14 Jul 2015, 00:57
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Solution -
A+B+C complete the job in 4 hours.
A+B complete the job in 5 hours.

A+B and C complete the job in 4 hours --> 1/(A+B) + 1/C = 1/4 -->1/5+1/C=1/4 ----> C=20 hours. ANS E
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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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14 Jul 2015, 03:16
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Let A,B,C denote the hours in which Anglea, Bernie and Colleen can finish the jobs individually.

Thus (1/A)+ (1/B)+(1/C) = 1/4 and (1/A)+(1/B) = 1/5 ----> 1/C = 1/20 ---> C = 20 Hours. Thus E is the correct answer.
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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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14 Jul 2015, 04:33
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Let, Total work = 20 Units

All working together, in 4 hours finish work = 20 Units
i.e. All working together, in 1 hour finish work = 20/4 = 5 Units

Angela and Bernie, working together at their respective rates, can complete in 5 hours = 20 Units
i.e. Angela and Bernie, working together at their respective rates, can complete in 1 hours = 20/5 = 4 Units

i.e. 1 hour work of Colleen = 5 - 4 = 1 Unit
i.e. Time taken by Colleen to finish 20 unit work = 20*1 = 20 days

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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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14 Jul 2015, 05:53
Let the work done by Angela (A), Bernie (B), and Colleen (C) per hour => 1/A + 1/B + 1/C = 1/4

1/A + 1/B = 1/5

So, 1/C = 1/4 - 1/5 = 5-4/20 = 1/20 = 20 hours. Ans (E).
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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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18 Jul 2015, 05:39
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Work done in one hour => 1/A + 1/B + 1/C = 1/4 and 1/A + 1/B = 1/5

Hence 1/C = 1/4 - 1/5 = 1/20 => C = 20 hours to complete the job alone

Option E
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Posts: 8792
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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18 Jul 2015, 05:43
1
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

one hour work of all three - one hour work of two other than C=one hour work of C..
$$\frac{1}{4}-\frac{1}{5}=\frac{1}{20}$$..
ans 20 E
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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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19 Jul 2015, 12:26
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

800score Official Solution:

If Angela, Bernie, and Colleen can complete a job in 4 hours, they can complete 1/4 of the job in an hour. Furthermore, if Angela and Bernie can complete the same job in 5 hours, they can do 1/5 of the entire job in an hour.

If the three of them can do 1/4 of a job in an hour, and without Colleen the other two can do 1/5 of a job in an hour, then the amount of the job Colleen can do in an hour is the difference of these results:
1/4 – 1/5 = 5/20 – 4/20 = 1/20.

Since Colleen can do 1/20 of the job in an hour, it will take her 20 hours to do the entire job by herself.

The correct answer is choice (E).
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Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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15 Apr 2020, 08:52
Top Contributor
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

For these kinds of work questions, it's often useful to assign a nice value to the entire job
We're looking for a value that works best with 4 hours and 5 hours.

So, let's say the entire job consists of making 20 widgets (works with 4 and 5)

Let A = the number of widgets that Angela can make in ONE HOUR
Let B = the number of widgets that Bernie can make in ONE HOUR
Let C = the number of widgets that Colleen can make in ONE HOUR

Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours.
The job consists of making 20 widgets
So, the COMBINED rate of all three people is 5 widgets per HOUR
In other words, A + B + C = 5

Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours.
So, the COMBINED rate of Angela and Bernie is 4 widgets per HOUR
In other words, A + B = 4

How long would it take Colleen, working alone, to complete the entire job?
If A + B + C = 5
and A + B = 4, then we can conclude that C = 1
In other words, Colleen can make 1 widget in ONE HOUR
The job consists of making 20 widgets

Time = output/rate

So, the time for Colleen to complete the entire job = 20/1
= 20 hours

Cheers,
Brent
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Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

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17 Apr 2020, 03:29
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

We can create the equation:

1/A + 1/B + 1/C = 1/4

Since 1/A + 1/B = 1/5, thus:

1/5 + 1/C = 1/4

1/C = 1/4 - 1/5

1/C = 5/20 - 4/20

1/C = 1/20

C = 20

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Angela, Bernie, and Colleen can complete a job, all working together,   [#permalink] 17 Apr 2020, 03:29