Question

A train coversa distanceof 300km at a uniform speed if the speed of the train increased by 5km /hour it takes 2hoursless in the journey find the original speed of the train

Answer 1

let the speed of the train = x km /h
Distance of the train = 300km
so time taken = distance/speed
300/x
when the speed increased by 5km/h ,(x+5)
so, time taken by train = 300/ (x+5)
Now , according to the question:
300/x -300/(x+5) = 2
300x - 300x +1500 = 2x^2 +10x
1500 = 2x^2 +10x
0 = 2x^2+10x-1500
0 = 2(x^2 +5x-750)
0= x^2 + 30x -25x - 750
0 = x( x+30) -25(x+30)
0 =(x-25) (x+30)
so x= 25 and x= -30
SO the original speed of train is 25 km