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 ?

Let the distance travelled by train be x km
Then, distance travelled by bus = (285 - x) km
$$\eqalign{ & \therefore \left( {\frac{{285 - x}}{{40}}} \right) + \frac{x}{{55}} = 6 \cr & \Leftrightarrow \frac{{\left( {285 - x} \right)}}{8} + \frac{x}{{11}} = 30 \cr & \Leftrightarrow \frac{{11\left( {285 - x} \right) + 8x}}{{88}} = 30 \cr & \Leftrightarrow 3135 - 11x + 8x = 2640 \cr & \Leftrightarrow 3x = 495 \cr & \Leftrightarrow x = 165 \cr} $$
Hence, distance travelled by train = 165 km