Question

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 ______.

Options

• $$x^2 - 8x - 1280 = 0$$

• $$x^2 + 8x + 1280 = 0$$

• $$x^2 - 8x + 1280 = 0$$

• $$x^2 + 8x - 1280 = 0$$

Answer 1

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 x² – 8x – 1280 = 0.

Explanation:

The time difference gives $$\frac{480}{x-8}-\frac{480}{x}=3$$. Simplifying yields the stated quadratic equation. The other options have incorrect signs and do not represent this time difference.