a hotel housekeeper has cleaned $\frac{1}{3}$ of the first floor in $\frac{1}{5}$ of an hour. at what rate…

a hotel housekeeper has cleaned $\frac{1}{3}$ of the first floor in $\frac{1}{5}$ of an hour. at what rate is she cleaning? simplify your answer and write it as a proper fraction, mixed number, or whole number. floors per hour

a hotel housekeeper has cleaned $\frac{1}{3}$ of the first floor in $\frac{1}{5}$ of an hour. at what rate is she cleaning? simplify your answer and write it as a proper fraction, mixed number, or whole number. floors per hour

Answer

Explanation:

Step1: Recall rate - formula

The rate formula is $r=\frac{work}{time}$. Here, the work is the fraction of the floor cleaned and the time is the time taken.

Step2: Substitute values

We know that the work $w = \frac{1}{3}$ (fraction of the floor cleaned) and the time $t=\frac{1}{5}$ (hours). So, $r=\frac{\frac{1}{3}}{\frac{1}{5}}$.

Step3: Divide by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. So, $r=\frac{1}{3}\times\frac{5}{1}=\frac{5}{3}$.

Step4: Convert to mixed - number

$\frac{5}{3}=1\frac{2}{3}$.

Answer:

$1\frac{2}{3}$