Question

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.

Answer 1

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☆Required Answer☆

Let the speed of the train be x km/hr.

Then time taken to travel a distance of:

$\mapsto480km = \frac{480}{x} hr$

Time taken by the train to travel a distance of 480km with the speed ( x - 8 ) km/hr

$\mapsto \frac{480}{x - 8} hr$

It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance

$∴ \frac{480}{x - 8} = \frac{480}{x} + 3 \\ \\ \implies \frac{480}{x - 8} - \frac{480}{x} = 3 \implies \frac{480(x - x + 8)}{x(x - 8)} = 3\implies \frac{480 \times 8}{x(x - 8)} = 3 \\ \\ \implies3x(x - 8) = 480 \times 8 \implies \: x(x - 8) = 160 \times 8 \implies {x}^{2} - 8x - 1280 = 0$

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