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प्रश्न
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.
उत्तर
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.
`480/x`
`480/(x - 8)`
`480/(x - 8) = 480/x + 3`
`480/(x - 8) - 480/x = 3`
`((480)(8))/((x - 8)(x)) = 3`
x2 − 8x − 1280 = 0
ax2 + 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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