Apply the problem-solving strategy for work applications to find how long it takes an individual to clean a house alone given the combined time. If Ra’shon can clean the house in $7$ hours alone, let $s$ be the number of hours his sister takes to clean it alone. In $1$ hour, Ra’shon completes $\frac{1}{7}$ of the job, and his sister completes $\frac{1}{s}$ of the job. Since it takes them $3$ hours working together, they complete $\frac{1}{3}$ of the job in $1$ hour. The rational equation is: $\frac{1}{7} + \frac{1}{s} = \frac{1}{3}$ Multiply both sides by the least common denominator, $21s$: 21s \left(\frac{1}{7} + \frac{1}{s} ight) = 21s \left(\frac{1}{3} ight) Distribute and simplify: $3s + 21 = 7s$ Subtract $3s$ from both sides: $21 = 4s$ Divide by $4$: $s = \frac{21}{4}$ Converting the improper fraction to a mixed number yields $5 \frac{1}{4}$ hours. Since $\frac{1}{4}$ of an hour is $15$ minutes, it would take Ra’shon’s sister $5$ hours and $15$ minutes to clean the house alone.