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. Find the speed of the train.

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Accepted Answer

Step 1: Let the speed of train be $x$ km/h. Reduced speed $= (x - 8)$ km/h.
Step 2: ATQ: $\frac{480}{x - 8} - \frac{480}{x} = 3$
Step 3: $\Rightarrow 480x - 480(x - 8) = 3x(x - 8) \Rightarrow 3840 = 3x^2 - 24x \Rightarrow x^2 - 8x - 1280 = 0$
Step 4: $(x - 40)(x + 32) = 0 \Rightarrow x = 40$ (rejecting $x = -32$ as speed cannot be negative)
Step 5: $	herefore$ Speed of train $= 40$ km/h

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