1. **State the problem:** Machine A can finish the job in 4 hours, and Machine B can finish the same job in 6 hours. We want to find how long it takes for both machines working together to complete the job. 2. **Calculate the rates:** Machine A's rate is $$\frac{1}{4}$$ jobs per hour. Machine B's rate is $$\frac{1}{6}$$ jobs per hour. 3. **Add the rates together:** When both machines work together, their combined rate is $$\frac{1}{4} + \frac{1}{6}$$ jobs per hour. 4. **Find common denominator and sum:** $$\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}$$ So, combined rate $$= \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$$ jobs per hour. 5. **Find total time to complete the job together:** Time $$t = \frac{1}{\text{combined rate}} = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4$$ hours. 6. **Interpretation:** Both machines working together will finish the printing job in 2.4 hours, or 2 hours and 24 minutes.