1. **Problem:** A first-class job done by an adult alone takes 6 hours. If a child helps, it takes 2 hours. How long will it take for the child to do the job alone? 2. **Formula and rules:** Work rate is the reciprocal of time. If the adult's rate is $\frac{1}{6}$ job/hour, and together they finish in 2 hours, their combined rate is $\frac{1}{2}$ job/hour. 3. **Step 1:** Let the child's rate be $r$ jobs/hour. 4. **Step 2:** The combined rate is adult rate plus child rate: $$\frac{1}{6} + r = \frac{1}{2}$$ 5. **Step 3:** Solve for $r$: $$r = \frac{1}{2} - \frac{1}{6} = \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$$ 6. **Step 4:** The child's time to finish alone is the reciprocal of $r$: $$\text{Time} = \frac{1}{r} = \frac{1}{\frac{1}{3}} = 3$$ hours. **Answer:** The child alone will finish the job in 3 hours.