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Angela, Bernie, and Colleen can complete a job, all working together,
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13 Jul 2015, 23:56
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93% (00:57) correct 7% (01:59) wrong based on 99 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,
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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,
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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,
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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 Answer: option E
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Re: Angela, Bernie, and Colleen can complete a job, all working together,
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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 = 54/20 = 1/20 = 20 hours. Ans (E).
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Re: Angela, Bernie, and Colleen can complete a job, all working together,
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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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Re: Angela, Bernie, and Colleen can complete a job, all working together,
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18 Jul 2015, 05:43
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,
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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,
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