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

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

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).

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

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

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).

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

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

Answer: E

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