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**Represent the following situation in the form of a 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.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

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#### Solution

`480/x`

`480/(x - 8)`

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

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

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

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

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