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Mathematics

Represent the following situation in the form of quadratic equation :

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.

Quadratic Equations

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Answer

Let speed of train be x km/hour.

By formula,

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

Given,

If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance.

∴480x−8−480x=3⇒480x−480(x−8)x(x−8)=3⇒480x−480x+3840x2−8x=3⇒3840=3(x2−8x)⇒3x2−24x=3840⇒3(x2−8x)=3840⇒x2−8x=38403⇒x2−8x=1280⇒x2−8x−1280=0.\therefore \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 3x^2 - 24x = 3840 \\[1em] \Rightarrow 3(x^2 - 8x) = 3840 \\[1em] \Rightarrow x^2 - 8x = \dfrac{3840}{3} \\[1em] \Rightarrow x^2 - 8x = 1280 \\[1em] \Rightarrow x^2 - 8x - 1280 = 0.

Hence, the required equation is x2 - 8x - 1280 = 0.

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