#### 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.

#### Solution

Let the speed of the fast train be x km/hrthen

the speed of the slow train be = (x - 10)km/hr

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

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

Therefore,

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

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

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

`rArr2000/(x^2-10x)=1`

⇒ 2000 = x^{2} - 10x

⇒ x^{2} - 10 - 2000 = 0

⇒ x^{2} - 50x + 40x - 2000 = 0

⇒ x(x - 50) + 40(x - 50) = 0

⇒ (x - 50)(x + 40) = 0

So, either

x - 50 = 0

x = 50

Or

x + 40 = 0

x = -40

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

Thus, when x = 50 then

= x - 10

= 50 - 10

= 40

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

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