A train crosses two bridges 370 m and 480 m long in 51 and 62 seconds…

Speed = \(\frac{ Distance}{ Time}\)

Let the length of the train be x

So, according to the question:

Speed =  \(\frac{ \text{x + 370}}{51}\) m/s  ---------1st equation

Speed =  \(\frac{\text{x + 480}}{62}\) m/s  ----------2nd equation

From 1st and 2nd equation:

\(\frac{ \text{x + 370}}{51}\) =  \(\frac{\text{x + 480}}{62}\)

62x + 22940 = 51x + 24480

11x = 1540

x = \(\frac{ 1540}{11 }\)

x = 140

Length of the train = 140 m

Speed of the train =  \(\frac{ \text{140 + 370}}{51}\)

Speed of the train =  \(\frac{ \text{510}}{51}\)

Speed of the train = 10 m/s 

Speed of train in km/hr = 10 x \(\frac{ 18}{5 }\) km/hr

Speed of train in km/hr = 36 km/hr