Step 1: Construct the equation based on given condition.
let the original speed of the train =x km/h.
Then the increased speed of the train
=(x+5)km/h.
and distance =360 km.
According to the question,
360x−360x+5=45
(∴speed=distancetime)
[∵48minutes=4860hours=45hours]
⇒360(x+5)−360xx(x+5)=45
⇒360x+1800−360xx(x+5)=45
⇒1800x2+5x=45
⇒1800×54=x2+5x
⇒x2+5x=1800×54=2250
⇒x2+5x−2250=0.
Step 2: Find the roots using factorization.
By splitting the middle term, we get :
x2+(50x−45x)−2250=0
⇒x2+50x−45x−2250=0
⇒x(x+50)−45(x+50)=0
⇒x(x+50)(x+45)=0
⇒x+50=0 or x−45=0
x≠−50 because speed can not be negative
So, x−45=0
⇒x=45
Hence, the original speed of the train is 45km/h.