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
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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
Thanks in advance.
