Question

a fast train takes one hour less than a slow train for a journey of 200 km if the speed of the slow train is 10 km/ h less that of the fast train find the speed of two train

Answer 1

let speed of fast train be x km/hr
speed of slower train = x - 10 km/hr

A/Q  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

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the speed of fast train be x km/h.

And the speed of slow train be (x - 10) km/h.

Time taken by the fast train to cover 200 km = 200/x hr.

Time taken by the slow train to cover 200 km = 200/x - 10 hr.

According to the Question,

⇒ 200/x - 200/x - 10 = 1

⇒ 200(x - 10) - 200x/x(x - 10) = 1

⇒ 200x - 2000 - 200x/x² - 10x = 1

⇒ x² - 10x = - 2000

⇒ x² - 10x + 2000 = 0

⇒ x² - 50x + 40x + 2000 = 0

⇒ x(x -50) + 40(x - 50) = 0

⇒ (x - 50) (x + 40) = 0

⇒ x = 50, - 40 (As speed can't be negative)

⇒ x = 50 km/h

Speed of fast train = x = 50 km/h

Speed of slow train = x - 10 = 50 - 10 = 40 km/h.