Let the speed of the train be ‘a’ km/hr and the actual time taken be ‘t’
Given, train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 4 hour less for the same journey.
Distance = speed × time
⇒ 360 = a × t
⇒ t = 360/a
Also, 360 = (a + 5)(t – 4)
\(\Rightarrow 360=(a+5)(\frac{360}{a}-4)\)
⇒ 360a = (a + 5)(360 – 4a)
⇒ 360a = 360a + 1800 – 4a2 – 20a
⇒ a2 + 5a – 450 = 0
Upon solving we will get a to be 18.86 and -23.86 but the speed can't be negative so the speed of the train is 18.86 km/hr.
