Let initial speed of the train be x km/h,
Then, time taken to cover 360 km
If the speed had been 5 km/h more, \(\frac{360}{x}\)Hr.
then time taken to cover is \(\frac{360}{x + 5}\) Hr.
x(x + 365) = 360 (x + 5)
x2 + 365x = 360x + 1800
x2 + 365x – 360x – 1800 = 0
x2 + 5x – 1800 = 0
x2 + 45x – 40x – 1800 = 0
x(x + 45) – 40 (x + 45) = 0
(x + 45) (x – 40) = 0
If x + 45 = 0, then x = – 45
If x – 40 = 0, then x = 40
∴ Initial speed of a train is 40 km/hr.