A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Let, the speed of train = x km/h
Distance = 360 km
Therefore, the time taken t₁ = 360/x hours [Because time = distance/speed]

If the speed had been 5 km/h more, than the t₂ = 360/x+5 hours
According to question,
360/x = 360/x+5 + 1
⇒ 360/x – 360/x + 5 = 1
⇒ 360(x + 5) – 360x/x(x+5) = 1

⇒ 360x + 1800 – 360x = x(x+5)
⇒ 1800 = x² + 5x
⇒ x² + 5x – 1800 = 0
⇒ x² + 45x – 40x – 1800 = 0
⇒ x(x + 45) – 40(x + 45) = 0
⇒ (x + 45)(x – 40) = 0
⇒ (x + 45) = 0 or (x – 40) = 0
Either x = – 45 or x = 40
But, x ≠ – 45, as x is the speed of train which can not be nagative.
So, x = 40
Hence, the speed of train is 40Km/h.