A person travels a distance of 240 km, partly by train and the rest by bus.He takes $3\frac{1}{2}$ hours if he travels 150 km by the train and the rest by bus. If he travels 140 km by bus and rest by train. He takes $3\frac{2}{3}$hours. What is the Speed of the tarin?

75 km/h

Let speed of train = T km/h & Speed of Bus = B km/h

According to question ,

\(\frac{150}{T}\) + \(\frac{90}{B}\) = \(\frac{7}{2}\)

\(\frac{50}{T}\) + \(\frac{30}{B}\) = \(\frac{7}{6}\)   ------(1)

In 2nd case,

\(\frac{100}{T}\) + \(\frac{140}{B}\) = \(\frac{11}{3}\)

\(\frac{50}{T}\) + \(\frac{70}{B}\) = \(\frac{11}{6}\)   ------(2)

Subtract equation 1 from equation 2

\(\frac{40}{B}\) = \(\frac{4}{6}\)

B = 60 km/h

By putting value of B in equation 1

\(\frac{50}{T}\) + \(\frac{30}{60}\) = \(\frac{7}{6}\)

\(\frac{50}{T}\) = \(\frac{7}{6}\) - \(\frac{1}{2}\) 

T = 75 km/h

So , speed of train is 75 km/h