A person travels 285 km in 6 hours in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hour. In the second part of the journey, he travels by train at the speed of 55 km per hour. How much distance did he travel by train?

### Concept & Logic Use a system of linear equations or a single variable equation splitting the total time across two different speeds. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * **Given:** * Total distance = $285$ km * Total time = $6$ hours * Speed of bus = $40$ km/hr * Speed of train = $55$ km/hr * **Equation Setup:** * Let the time travelled by train be $t$ hours. * Then, time travelled by bus = $(6 - t)$ hours. * Distance by train + Distance by bus = Total Distance * $55t + 40(6 - t) = 285$ * **Solve for $t$:** * $55t + 240 - 40t = 285$ * $15t = 45$ * $t = 3$ hours * **Calculate Train Distance:** * Distance by train = Speed $\times$ Time = $55 \times 3 = 165$ km. ### Exam Strategy & Shortcut Use the Alligation method. Average speed for the whole trip = $\frac{285}{6} = 47.5$ km/hr. Bus speed (40) ............. Train speed (55) ................. Avg (47.5) ................. (55 - 47.5) = 7.5 ........ (47.5 - 40) = 7.5 Ratio of times = $7.5 : 7.5 = 1 : 1$. This means time is divided equally: $3$ hours bus, $3$ hours train. Distance by train = $55 \times 3 = 165$ km. ### Common Pitfall Calculating the distance traveled by bus ($120$ km) and accidentally selecting it if it were an option, instead of the required train distance. ### Final Answer Therefore, the correct answer is **165 km**.