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The speed of an express train is x km/h and the speed of an ordinary train is 12 km /h less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km , find the speed of the express train.

Quadratic Equations

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Answer

Speed of an express train is x km/h

So, the speed of ordinary train is (x - 12) km/h

Given, ordinary train takes one hour longer than express train to cover 240 km

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

∴240x−12−240x=1⇒240x−240(x−12)x(x−12)=1⇒240x−240x+2880=x(x−12)⇒2880=x2−12x⇒x2−12x−2880=0⇒x2−60x+48x−2880=0⇒x(x−60)+48(x−60)=0⇒(x−60)(x+48)=0⇒x−60=0 or x+48=0⇒x=60 or x=−48\therefore \dfrac{240}{x - 12} - \dfrac{240}{x} = 1 \\[1em] \Rightarrow \dfrac{240x - 240(x - 12)}{x(x - 12)} = 1 \\[1em] \Rightarrow 240x - 240x + 2880 = x(x - 12) \\[1em] \Rightarrow 2880 = x^2 - 12x \\[1em] \Rightarrow x^2 - 12x - 2880 = 0 \\[1em] \Rightarrow x^2 - 60x + 48x - 2880 = 0 \\[1em] \Rightarrow x(x - 60) + 48(x - 60) = 0 \\[1em] \Rightarrow (x - 60)(x + 48) = 0 \\[1em] \Rightarrow x - 60 = 0 \text{ or } x + 48 = 0 \\[1em] \Rightarrow x = 60 \text{ or } x = -48

Since speed of train cannot be negative hence, x ≠ -48

Hence, the speed of express train is 60 km/h.

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