1. Stating the problem: Plumber A can install a bathroom in 12 hours, and Plumber B can do it in 8 hours. We want to find how long it takes if they work together. 2. Calculate individual rates: - Plumber A's rate is $\frac{1}{12}$ bathroom per hour. - Plumber B's rate is $\frac{1}{8}$ bathroom per hour. 3. Add their rates to get combined rate: $$ \frac{1}{12} + \frac{1}{8} = \frac{2}{24} + \frac{3}{24} = \frac{5}{24} $$ bathrooms per hour. 4. Find the time taken working together by taking the reciprocal of the combined rate: $$ t = \frac{1}{\frac{5}{24}} = \frac{24}{5} = 4.8 $$ hours. 5. Conclusion: If both plumbers work together, it will take them 4.8 hours to install the bathroom.