Given:
A train travels 288 km at a uniform speed.
If the speed has been 4 km per hour more it would have taken one hour less for the same journey.
To find:
The initial speed of the train.
Solution:
Let x km/h be the initial speed on the train.
New speed of train = (x+4) km/h
We know that,
[tex]Time=\dfrac{Distance}{Speed}[/tex]
Time taken by the train initially to cover 288 km is [tex]\dfrac{288}{x}[/tex] hours.
New time taken by the train to cover 288 km is [tex]\dfrac{288}{x+4}[/tex] hours.
It is given that If the speed has been 4 km per hour more it would have taken one hour less for the same journey.
[tex]\dfrac{288}{x}-\dfrac{288}{x+4}=1[/tex]
[tex]\dfrac{288(x+4)-288x}{x(x+4)}=1[/tex]
[tex]288x+1152-288x=x^2+4x[/tex]
[tex]1152=x^2+4x[/tex]
[tex]0=x^2+4x-1152[/tex]
Splitting the middle term, we get
[tex]x^2+36x-32x-1152=0[/tex]
[tex]x(x+36)-32(x+36)=0[/tex]
[tex](x+36)(x-32)=0[/tex]
[tex]x=-36,32[/tex]
We know that the speed cannot be negative. So, the only possible value of x is 32.
Therefore, the speed of the train is 32 km/h.
