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Bea can paint a house three times faster than Alice can paint a house.

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Bea can paint a house three times faster than Alice can paint a house. [#permalink]

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New post 15 Jan 2018, 04:50
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Question Stats:

84% (01:46) correct 16% (01:13) wrong based on 45 sessions

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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
[Reveal] Spoiler: OA

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Re: Bea can paint a house three times faster than Alice can paint a house. [#permalink]

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New post 15 Jan 2018, 05:19
Rate of Bea (Rb) = 3 * Rate of Alice (Ra)

(Ra + Rb) * T = W
4(Ra) = 1/24

Ra = 1/96

Rb = 3*(1/96) = 1/32

Time taken by Bea = 32 hrs.

Answer: C
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Re: Bea can paint a house three times faster than Alice can paint a house. [#permalink]

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New post 15 Jan 2018, 09:55
Bunuel 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


Efficiency of Bea = 3
Efficiency of Alice = 1

Combined efficiency of Alice and Bea = 4

So, Total work is 24*4 = 96 units

Time required by Bea to complete the work is 96/3 = 32 Hours, answer will be (C)

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Re: Bea can paint a house three times faster than Alice can paint a house. [#permalink]

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New post 15 Jan 2018, 12:30
Bunuel 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=hours B takes to paint house alone
working with A, B paints 3/4:1/4 of house
(3/4)/24=1/b
b=32
C
Re: Bea can paint a house three times faster than Alice can paint a house.   [#permalink] 15 Jan 2018, 12:30
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Bea can paint a house three times faster than Alice can paint a house.

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