Question

Archer, Brian, and Camille can clean a house. Archer can clean the house one hour faster than Brian, and Brian takes twice as long as Camille to clean the house. If Archer and Camille work together to clean a house, it takes 5 hours. To the nearest thousandth of an hour, how long would it take Brian to clean the house working alone?

Answer 1

Brian would take approximately 4.000 hours to clean the house working alone.

Here's how to solve the problem:

Identify variables:

Let C be the time it takes Camille to clean the house alone (in hours).

Brian takes twice as long as Camille, so Brian's time is 2C.

Archer cleans one hour faster than Brian, so Archer's time is 2C - 1.

Use the given information:

We know that Archer and Camille together can clean the house in 5 hours: C + (2C - 1) = 5

Solve for C:

Combine like terms: 3C - 1 = 5

Add 1 to both sides: 3C = 6

Divide both sides by 3: C = 2

Find Brian's time:

Since Brian takes twice as long as Camille, his time is 2C = 2 * 2 = 4 hours.

Therefore, Brian would take approximately 4.000 hours to clean the house working alone.