1. **State the problem:** Two trains leave the station at the same time, one heading east at 95 mph and the other west at 75 mph. We need to find the time $t$ in hours when they are 408 miles apart. 2. **Formula used:** The distance between two objects moving in opposite directions is the sum of the distances each travels. Distance = Speed \times Time. 3. **Set up the equation:** Let $t$ be the time in hours. $$\text{Distance apart} = (95)(t) + (75)(t) = 408$$ 4. **Combine like terms:** $$95t + 75t = 408$$ $$170t = 408$$ 5. **Solve for $t$:** $$t = \frac{408}{170}$$ 6. **Simplify the fraction:** $$t = \frac{\cancel{408}^{24} \times 17}{\cancel{170}^{10} \times 17} = \frac{24}{10}$$ 7. **Final simplification:** $$t = \frac{24}{10} = 2.4$$ **Answer:** It will take $2.4$ hours for the two trains to be 408 miles apart.