Share

Books Shortlist

# 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. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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 = x2 - 10x

⇒ x2 - 10 - 2000 = 0

⇒ x2 - 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.

Is there an error in this question or solution?

#### APPEARS IN

Solution 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. Concept: Solutions of Quadratic Equations by Factorization.
S