Question

A fast train takes 3 hours less than a slow train in travelling 600 km. If the speed of fast train is 10 km/hr. more than the speed of slow train, find the speed of boththe trains.

Answer 1

Solution:-
Let the speed of the slow train be 'x' km/hr and the speed of the fast train be (x+10) km/hr.
Time taken by the slow train to cover the distance of 600 km = (600/x) hours
Time taken by the fast train to cover the distance of 600 km = 600/(x+10) hours.
Now, according to the question.
(600/x) - 600/(x+10) = 3
{600(x+10) - 600x}/x(x+10) = 3
600x + 6000 - 600x = 3{x(x+10)}
6000 = 3x² + 30x
3x² + 30x - 6000 = 0 Dividing it by 3 we get
x² + 10x - 2000
x² + 50x - 40x - 2000 = 0
x(x+50) - 40(x+50) = 0
(x-40) (x+50)
x = 40 or x = -50
x = -5 is not possible, the speed cannot be in negative.
So, x = 40
Speed of the slow train is 40 km/hr and the speed of the fast train is 40 + 10 = 50 km/hr.
Answer. 

Answer 2

Answer:

Step-by-step explanation:

Solution :-

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

And the speed of the fast train be (x + 10) km/h.

Time taken by slow train to cover 600 km = 600/x hrs

Time taken by fast train to cover 600 km = 600/(x + 10) hrs.

According to the Question,

⇒ 600/x + 600/(x + 10) = 3

⇒ 600(x + 10) - 600x/x(x + 10) = 3

⇒ 600/x² + 10x = 3

⇒ 3(x² + 10x) = 6000

⇒ x² + 10x - 2000 = 0

By using factorization method, we get

⇒ 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, 40 (As speed can't be negative)

⇒ x = 40 km/h

Speed of slow train = x = 40 km/h

Speed of fast train = x + 10 = 40 + 10 = 50 km/h