a train travels a distance of 480 km at a uniform speed If the speed had been 8 - Maths - Quadratic Equations

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 hrs more to
cover the same distance we need to find the speed of the train

Santosh Kumar · Accepted Answer

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

Given, distance covered by the train = 480 km

∴ Original time taken by train $= \frac{480}{x}$ hr

If the speed of the train had been 8 km/hr less, then

New speed of the train = (x – 8) km/hr

∴ New time taken by the train $= \frac{480 km}{(x - 8) km/hr} = \frac{480}{x - 8} hr$

Given, New time taken by train – Original time taken by train = 3

$∴ \frac{480}{x - 8} - \frac{480}{x} = 3 \Rightarrow \frac{480 [x - (x - 8)]}{x (x - 8)} = 3 \Rightarrow 480 (x - x + 8) = 3 x (x - 8) \Rightarrow 3 x^{2} - 24 x - 3840 = 0 \Rightarrow x^{2} - 8 x - 1280 = 0 \Rightarrow x^{2} - 40 x + 32 x - 1280 = 0 \Rightarrow x (x - 40) + 32 (x - 40) = 0 \Rightarrow (x + 32) (x - 40) = 0 \Rightarrow x + 32 = 0 o r x - 40 = 0 \Rightarrow x = - 32 or x = 40$

∴ x = 40 (Speed of the train cannot be negative)

Thus, the original speed of the train is 40 km/hr.

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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 hrs more to cover the same distance . we need to find the speed of the train.