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/hr less than that of the fast train, find the speed of the two trains.

Answer 1

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

The speed of the slow train is (x − 10) km/hr.

Using the formula:

Time = `"Distance"/"Speed"`

Time taken by the fast train to cover 200 km (T₁) = `200/xhr`

Time taken by the slow train to cover 200 km (T₂) =`200/(x-10)hr`

∴ `200/(x - 10) - 200/x = 1`

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

`rArr (200x - 200x + 2000)/(x^2-10x) = 1`

`rArr 2000/(x^2 - 10x) = 1`

⇒ 2000 = x² − 10x

⇒ x² − 10x − 2000 = 0

⇒ x² − 50x + 40x − 2000 = 0

⇒ x(x − 50) + 40(x − 50) = 0

⇒ (x − 50)(x + 40) = 0

x − 50 = 0 or x + 40 = 0

x = 50 or x = −40

But, the speed of the train can never be negative.

Thus, when x = 50 

The speed of the slow train is x − 10 = 50 − 10

= 40

Hence, the speed of the fast train is x = 50 km/hr

The speed of the slow train is x = 40 km/hr respectively.