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Angela, Bernie, and Colleen can complete a job, all working
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22 Apr 2020, 12:34
22 Apr 2020, 12:34
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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
A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours
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Given Kudos: 136
Re: Angela, Bernie, and Colleen can complete a job, all working
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22 Apr 2020, 12:54
22 Apr 2020, 12:54
Carcass 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
A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours
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
Answer: E
Cheers,
Brent
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Status:Founder & Quant Trainer
Affiliations: Prepster Education
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Location: India
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Re: Angela, Bernie, and Colleen can complete a job, all working
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03 Feb 2021, 07:43
03 Feb 2021, 07:43
Let,
Angela's time = A
Bernie's time = B
Colleen's time = C
Therefore, 1/A + 1/B + 1/C = 1/4 ........ (1)
Also,
Angela and Bernie, working together can complete the same job in 5 hours
i.e. 1/A + 1/B = 1/5 ......... (2)
Putting 2 in 1;
1/5 + 1/C = 1/4
1/C = 1/20
C = 20
Hence, option E
Angela's time = A
Bernie's time = B
Colleen's time = C
Therefore, 1/A + 1/B + 1/C = 1/4 ........ (1)
Also,
Angela and Bernie, working together can complete the same job in 5 hours
i.e. 1/A + 1/B = 1/5 ......... (2)
Putting 2 in 1;
1/5 + 1/C = 1/4
1/C = 1/20
C = 20
Hence, option E
