Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone?

A) 28

B) 30

C) 32

D) 36

E) 40

The correct answer is C. I tried many ways, but I don't really get the right answer.

Maybe someone can help Thanks in advance.

## Quant - Work problem

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### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.mhoi wrote:Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone?

A) 28

B) 30

C) 32

D) 36

E) 40

Let B = number of hours it takes Bea to paint the house.

So, 3B = number of hours it takes Alice to paint the house

*[since Bea is three times faster than Alice]*

Now examine what can be accomplished in

**1 hour**

If Bea takes B hours to paint the entire house, then after 1 hour, Bea will have painted 1/B of the house.

If Alice takes 3B hours to paint the entire house, then after 1 hour, Alice will have painted 1/3B of the house.

If Alice and Bea work together, then the fraction of the house painted in

**1 hour**= 1/B + 1/3B

= 3/3B + 1/3B

= 4/3B

Now consider the fact that we're told that

*Working together, it takes Alice and Bea 24 hours to paint a house*So, in

**one hour**, Alice and Bea can paint 1/24 of a house

We can now write: 4/3B = 1/24

Cross-multiply to get: (4)(24) = (3B)(1)

Evaluate: 96 = 3B

Solve: B = 32

Answer: B

Cheers,

Brent

- GMATGuruNY
- GMAT Instructor
**Posts:**15539**Joined:**Tue May 25, 2010 12:04 pm**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1906 members**GMAT Score:**790

Since Bea paints 3 times faster than Alice, for every unit Alice paints, Bea paints 3 units.mhoi wrote:Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone?

A) 28

B) 30

C) 32

D) 36

E) 40

Thus, when Alice and Bea work together, of every 4 units painted, Alice paints 1 unit, while Bea paints 3 units.

Let the house = 96 units.

Combined rate for Bea and Alice = w/t = 96/24 = 4 units per hour.

Of the 4 units painted every hour, Bea paints 3 units, implying that Bea's rate = 3 units per hour.

Thus, the time for Bea alone = w/r = 96/3 = 32 hours.

The correct answer is C.

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Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

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### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

Here's another approach:mhoi wrote:Bea can paint a house three times faster than Alice can paint a house. If, working together, it takes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone?

A) 28

B) 30

C) 32

D) 36

E) 40

**Bea can paint a house three times faster than Alice can paint a house.**So, for every drop of paint that Alice applies, Bea applies 3 drops.

So, when they work together, we can say that, for every 4 drops of paint they apply, Bea applies 3 of those drops.

In other words, BEA DOES 3/4 OF THE WORK.

*I*

**t takes Alice and Bea 24 hours to paint a house**If Bea does 3/4 of the works, we know that, in 24 hours, Bea has painted 3/4 of the house.

In other words, every 8 hours, Bea paints 1/4 of the house.

So, it will take Bea 32 hours to paint the entire house.

Answer: C

Cheers,

Brent