Question

a train travels 288km at a uniform speed.if the speed has been 4km per hour more it would have taken one hour less for the same journey.find the speed of train​

Answer 1

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,

$Time=\dfrac{Distance}{Speed}$

Time taken by the train initially to cover 288 km is $\dfrac{288}{x}$ hours.

New time taken by the train to cover 288 km is $\dfrac{288}{x+4}$ 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.

$\dfrac{288}{x}-\dfrac{288}{x+4}=1$

$\dfrac{288(x+4)-288x}{x(x+4)}=1$

$288x+1152-288x=x^2+4x$

$1152=x^2+4x$

$0=x^2+4x-1152$

Splitting the middle term, we get

$x^2+36x-32x-1152=0$

$x(x+36)-32(x+36)=0$

$(x+36)(x-32)=0$

$x=-36,32$

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.