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Bunuel
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Bunuel Thank you.
Bunuel
Mahendra1996
Bunuel, kindly provide how can statement B can independently give the answer?
Bunuel
How long does it take Andrea to complete a job?

(1) Working together, Andrea, Benjamin, and Cheryl can complete the job in 30 minutes, and working together, Benjamin and Cheryl can complete the job in 80 minutes.

(2) The ratio of the time it takes Andrea to complete the job working alone, to the time it takes Cheryl to complete the job working alone, is 1 to 5, and working together Andrea and Cheryl can complete the job in 40 minutes.


­

(2) The ratio of the time it takes Andrea to complete the job working alone, to the time it takes Cheryl to complete the job working alone, is 1 to 5, and working together Andrea and Cheryl can complete the job in 40 minutes.

Assuming the time it takes Andrea to complete the job alone is x, and the time it takes Cheryl to complete the job is y, we have x/y = 1/5, which gives y = 5x.

Working together Andrea and Cheryl can complete the job in 40 minutes means 1/x + 1/y = 1/40.

So, we have two distinct linear equations with two unknowns: y = 5x and 1/x + 1/y = 1/40. We can solve and get the values of both x and y: x = 48, and y = 240.

Hope it's clear.
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Bunuel , could you explain statement 1
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How long does it take Andrea to complete a job?

(1) Working together, Andrea, Benjamin, and Cheryl can complete the job in 30 minutes, and working together, Benjamin and Cheryl can complete the job in 80 minutes.

(2) The ratio of the time it takes Andrea to complete the job working alone, to the time it takes Cheryl to complete the job working alone, is 1 to 5, and working together Andrea and Cheryl can complete the job in 40 minutes.


Bunuel , could you explain statement 1

Assuming the rates of Andrea, Benjamin, and Cheryl are a, b, and c respectively, we have the following equations:

  • a + b + c = 1/30 (their combined rate of work).
  • b + c = 1/80 (the combined rate of Benjamin and Cheryl).

Subtracting the second equation from the first gives:

a = 1/30 - 1/80 = 1/48.

Since the rate is the reciprocal of the time, the time needed for Andrea to complete the job is 48 minutes.

Hope it's clear.
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