Q2.    Represent the following situations in the form of quadratic equations :

            (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Answers (1)

Let the speed of the train be 's' km/h.

The distance to be covered by the train is 480\ km.

\therefore The time taken will be 

=\frac{480}{s}\ hours

If the speed had been 8\ km/h less, the time taken would be: \frac{480}{s-8}\ hours.

Now, according to question

\frac{480}{s-8} - \frac{480}{s} = 3 

\Rightarrow \frac{480x - 480(x-8)}{(x-8)x} = 3

\Rightarrow 480x - 480x+3840 = 3(x-8)x

\Rightarrow 3840 = 3x^2-24x

\Rightarrow 3x^2 -24x-3840 = 0

Dividing by 3 on both the side 

x^2 -8x-1280 = 0

Hence, the speed of the train satisfies the quadratic equation x^2 -8x-1280 = 0