1. **State the problem:** Kevin can clean a room alone in 36 minutes. When Ben helps, it takes 9 minutes together. We need to find how long it takes Ben to clean alone. 2. **Define variables:** Let $t$ be the time in minutes for Ben to clean the room alone. 3. **Work rates:** Kevin's rate is $\frac{1}{36}$ rooms per minute. Ben's rate is $\frac{1}{t}$ rooms per minute. 4. **Combined rate:** Working together, their rate is $\frac{1}{9}$ rooms per minute. 5. **Set up equation:** Sum of individual rates equals combined rate: $$\frac{1}{36} + \frac{1}{t} = \frac{1}{9}$$ 6. **Solve for $t$:** \begin{align*} \frac{1}{t} &= \frac{1}{9} - \frac{1}{36} \\ &= \frac{4}{36} - \frac{1}{36} \\ &= \frac{3}{36} \\ &= \frac{1}{12} \end{align*} 7. **Conclusion:** Ben's rate is $\frac{1}{12}$ rooms per minute, so Ben takes $t=12$ minutes alone to clean the room. **Final answer:** It would take Ben 12 minutes to clean the room alone.