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?
Answer & explanation
Correct answer: option 2
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