Apply the problem-solving strategy for work applications to find how long it takes an individual to paint a room alone. If Alice can paint the room in $6$ hours alone, let $t$ be the number of hours it takes Kristina to paint it alone. In $1$ hour, Alice paints $\frac{1}{6}$ of the room, and Kristina paints $\frac{1}{t}$ of the room. Since it takes them $4$ hours working together, their combined rate is $\frac{1}{4}$ of the room per hour. The rational equation is: $\frac{1}{6} + \frac{1}{t} = \frac{1}{4}$ Multiply both sides by the least common denominator, $12t$: 12t \left(\frac{1}{6} + \frac{1}{t} ight) = 12t \left(\frac{1}{4} ight) Distribute and simplify: $2t + 12 = 3t$ Subtract $2t$ from both sides: $t = 12$ It would take Kristina $12$ hours to paint the room by herself.