Angela, Bernie, and Colleen can complete a job, all. . . . .

M7MBA 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

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

M7MBA 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

We can create the equations:

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

1/A + 1/B = 1/5

Thus, 1/C = 1/4 - 1/5 = 5/20 - 4/20 = 1/20.

Since a person’s time to complete a job is the inverse of his or her rate, it takes Colleen 20 hours to complete the job.

Answer: E