Quadratic Equations (C10)

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of slower train is 10 km/hr less than that of faster train, find the speeds of two trains.

Answer

Let the speed of faster train be x km/hr.

∴ Speed of slower train = (x – 10) km/hr

200/(x - 10) - 200/x = 1

⇒ x2 – 10x – 2000 = 0

⇒ (x – 50) (x + 40) = 0

x = 50, –40 (rejected)

∴ Speed of faster train 50 km / hr

Speed of slower train 40 km / hr