One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?
A) $\frac{3}{4} \mathrm{hr}$
B) $4 \mathrm{hr}$
C) $5 \mathrm{hr}$
D) $3 \mathrm{hr}$

Question

Quizplus · Accepted Answer

Let the slower maid take $x$ hours to clean the house alone. Then the faster maid takes $\frac{x}{3}$ hours. Their combined rate is $\frac{1}{x} + \frac{3}{x} = \frac{4}{x}$. Given they clean the house together in 3 hours, $\frac{4}{x} = \frac{1}{3}$. Solving for $x$, we get $x = 12$. Thus, the faster maid takes $\frac{12}{3} = 4$ hours alone.

One Maid Can Clean the House Three Times Faster Than 34hr\frac{3}{4} \mathrm{hr}43​hr

One Maid Can Clean the House Three Times Faster Than $\frac{3}{4} \mathrm{hr}$