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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