Question

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

Answer 1

Let speed of fast train be x km/hr
speed of slower train = x - 10 km/hr
Given fast train takes 1 hr less than slower one in covering 200 km
⇒ 200/ x = 200/x-10 - 1
⇒ 200/x = 200 - (x-10) / x-10
⇒ 200(x-10) = 200x - x (x-10)
⇒200x-2000 = 200x - x² + 10x
⇒x² - 10x - 2000 = 0
⇒ x² -50x + 40x -2000 = 0 ⇒ (x-50)(x+40) = 0
x = 50 and x= - 40
since x can't be negative , so x= speed of faster train = 50 km/hr
speed of slower train = 40 km/hr