1. **State the problem:** Sam, Ton, and Paul together can finish a job in 3 hours. Sam alone can finish in 6 hours, and Ton alone in 8 hours. We need to find how long Paul alone will take to finish the job. 2. **Define rates:** The rate of work is \( \text{work done per hour} \). - Sam's rate: \( \frac{1}{6} \) (job/hour) - Ton's rate: \( \frac{1}{8} \) (job/hour) - Combined rate of Sam, Ton, and Paul: \( \frac{1}{3} \) (job/hour) 3. **Set up equation:** Let Paul's rate be \( \frac{1}{p} \) (job/hour). The sum of their rates is: $$ \frac{1}{6} + \frac{1}{8} + \frac{1}{p} = \frac{1}{3} $$ 4. **Solve for \( \frac{1}{p} \):** Calculate \( \frac{1}{6} + \frac{1}{8} \) first: $$ \frac{1}{6} = \frac{4}{24}, \quad \frac{1}{8} = \frac{3}{24} \implies \frac{1}{6} + \frac{1}{8} = \frac{4}{24} + \frac{3}{24} = \frac{7}{24} $$ Therefore: $$ \frac{7}{24} + \frac{1}{p} = \frac{1}{3} $$ Subtract \( \frac{7}{24} \) from both sides: $$ \frac{1}{p} = \frac{1}{3} - \frac{7}{24} = \frac{8}{24} - \frac{7}{24} = \frac{1}{24} $$ 5. **Find \( p \):** $$ p = 24 $$ **Answer:** Paul alone can finish the job in 24 hours.