Represent the following situations in the form of quadratic equations.

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.

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#### Solution

Let the speed of train be

*x*km/h.Time taken to travel 480 km = 480/

*x*km/hIn second condition, let the speed of train = (*x* - 8) km/h

It is also given that the train will take 3 hours to cover the same distance.

Therefore, time taken to travel 480 km = `(480/x + 3) `

Speed × Time = Distance

`(x - 8)(480/x + 3) = 480`

`⇒ 480 + 3x - 3840/x - 24 = 480`

⇒ 3*x* - 3840/*x* = 24

⇒ 3*x*^{2 }- 24*x* - 3840 = 0

⇒ x^{2} - 8x - 1280 = 0

Concept: Quadratic Equations

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