A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. If the initial speed of the train is x km/hr, then representation of this information algebraically is :

1. x² − 8x − 1280 = 0

2. x² + 8x + 1280 = 0

3. x² − 8x + 1280 = 0

4. x² + 8x − 1280 = 0

By formula,

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

Initial speed of train = x km/hr

Time taken to cover 480 km = $\dfrac{480}{x}$ hrs

Reduced speed of train = (x - 8) km/hr

Time taken to cover 480 km = $\dfrac{480}{x - 8}$ hrs

Given,

On reducing speed the time taken is 3 hours more.

$\Rightarrow \dfrac{480}{x - 8} - \dfrac{480}{x} = 3 \\[1em] \Rightarrow \dfrac{480x - 480(x - 8)}{x(x - 8)} = 3 \\[1em] \Rightarrow \dfrac{480x - 480x + 3840}{x^2 - 8x} = 3 \\[1em] \Rightarrow 3840 = 3(x^2 - 8x) \\[1em] \Rightarrow 3840 = 3x^2 - 24x \\[1em] \Rightarrow 3x^2 - 24x - 3840 = 0 \\[1em] \Rightarrow 3(x^2 - 8x - 1280) = 0 \\[1em] \Rightarrow x^2 - 8x - 1280 = 0.$

Hence, option 1 is the correct option.