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Sum

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 the train be x km/h.

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

In 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`

⇒ 3x - 3840/x = 24

⇒ 3x^{2} - 24x - 3840 = 0

⇒ x^{2} - 8x - 1280 = 0

⇒ ax^{2} + bx + c = 0

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

x = `(8 ± sqrt(64 + 4(1280)))/2`

= `(8 ± 72)/2`

= 40 km/hr

Concept: Quadratic Equations

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