1. **State the problem:** Nadya and Emma travel the same distance $y$. Nadya travels by train at 135 mph, Emma by bus at 60 mph. Emma takes 2 hours longer than Nadya. The time Nadya takes is $x$ hours. 2. **Formulate the system of equations:** - Nadya's time: $x$ - Emma's time: $x + 2$ - Distance formula: $\text{distance} = \text{speed} \times \text{time}$ 3. **Write equations for each traveler:** - Nadya: $y = 135x$ - Emma: $y = 60(x + 2)$ 4. **Identify the correct system:** This matches option A: $$\begin{cases} y = 135x \\ y = 60(x + 2) \end{cases}$$ 5. **Solve for $x$:** Set the two expressions for $y$ equal: $$135x = 60(x + 2)$$ 6. **Expand and simplify:** $$135x = 60x + 120$$ 7. **Subtract $60x$ from both sides:** $$135x - 60x = 120$$ $$\cancel{135}x - \cancel{60}x = 120$$ $$75x = 120$$ 8. **Solve for $x$:** $$x = \frac{120}{75} = \frac{24}{15} = \frac{8}{5} = 1.6$$ hours 9. **Find the distance $y$ using Nadya's equation:** $$y = 135x = 135 \times 1.6 = 216$$ miles **Final answers:** - Part A: Option A - Part B: Distance traveled is 216 miles