Quant - Work problem

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Quant - Work problem

by mhoi » Thu Jul 25, 2013 7:08 am
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.

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by vishugogo » Thu Jul 25, 2013 7:28 am
If Alice takes 3x hours

Bea takes x hours

1/x + 1/3x = 24

x=32

hopes this helps!!

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by Brent@GMATPrepNow » Thu Jul 25, 2013 7:42 am
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
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.


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

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by GMATGuruNY » Thu Jul 25, 2013 10:05 am
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
Since Bea paints 3 times faster than Alice, for every unit Alice paints, Bea paints 3 units.
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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by Brent@GMATPrepNow » Thu Jul 25, 2013 10:16 am
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
Here's another approach:

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.

It 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

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by mhoi » Fri Jul 26, 2013 7:45 am
Thank you a lot. Now I understood :-)