Working together, Cara and Cindy can rake the yard in $4$ hours. Working alone, Cindy takes $6$ hours. How long would it take Cara to rake the yard alone?

Let $t$ be Cara's solo time. The combined-rate equation: $\tfrac{1}{6} + \tfrac{1}{t} = \tfrac{1}{4}$. Isolate $\tfrac{1}{t}$: $\tfrac{1}{t} = \tfrac{1}{4} - \tfrac{1}{6} = \tfrac{3}{12} - \tfrac{2}{12} = \tfrac{1}{12}$. So $t = 12$ hours. Check: $\tfrac{1}{6} + \tfrac{1}{12} = \tfrac{2}{12} + \tfrac{1}{12} = \tfrac{3}{12} = \tfrac{1}{4}$ ✓. - Trap A ($2 = 6 - 4$) subtracts times — wrong model. - Trap B ($8$) gives a combined rate of $\tfrac{1}{6} + \tfrac{1}{8} = \tfrac{7}{24}$ per hour, joint time $\tfrac{24}{7} \approx 3.4$ hr $\ne 4$. - Trap C ($10$) miss-by-2 from the right answer. Observation: Cara is *slower* than Cindy (12 vs 6 hours alone) yet still helps reduce the joint time from 6 to 4 hours. Any positive rate added to a positive rate produces a faster combined time.