Question

A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 5km an hour, the journey would have taken 2 hours less. Find the original speed of the train

Answer 1

Let the spees of the train be v and the distance which have to cover be x and time taken be t
.
Given
x=300km
In first case train have to cover 300km in the hours.
speed the train,(v) = 300/t..............(1)
In second case ,

speed had been 5km/h more, then it would have taken 2 hours less to cover the same distance.
so speed= v+5
time = t-2 hours.
So ,
speed of train ,
v+5 = 300/(t-2).........................(2).
see picture!
speed of train=25 km/hr.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

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

Time taken by train to cover = 300/x hrs.

Increased speed = 5 km/h

Time taken to cover 300 km when speed is increased = 300/(x + 5) hrs.

According to the Question,

⇒ 300/x - 300/(x + 5) = 2

⇒ 300(x + 5) - 300x/x(x + 5) = 2

⇒ 300x + 1500 - 300x/x² + 5x = 2

⇒ 2x² + 10x = 1500

⇒ x² + 5x - 750 = 0

By using factorization method, we get

⇒ x² + 30x - 25 - 750 = 0

⇒ x(x + 30) - 25(x + 30) = 0

⇒ (x + 30) (x - 25) = 0

⇒ x + 30 = 0 or x - 25 = 0

⇒ x = - 30, 25 (As x can't be negative)

⇒ x = 25 km/h

Hence, the original speed of train is 25 km/h.