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# Represent the following situations in the form of quadratic equations: (iv) 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. Q.2(4)

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The question of class 10th exercise 4.1 of 2(4). The easiest way to solve this question is Represent the following situations in the form of quadratic equations: (iv) 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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1. Let us consider,

The speed of train = xÂ  km/h

And

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

As per second condition, the speed of train = (xÂ â€“ 8) km/h

Also given, the train will take 3 hours to cover the same distance.

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

As we know,

Speed Ã— Time = Distance

Therefore,

(xÂ â€“ 8)(480/(xÂ + 3) = 480

â‡’ 480Â + 3xÂ â€“ 3840/xÂ â€“ 24 = 480

â‡’ 3xÂ â€“ 3840/xÂ = 24

â‡’ 3x2Â â€“ 8xÂ â€“ 1280 = 0

Therefore, the speed of the train, satisfies the quadratic equation, 3x2Â â€“ 8xÂ â€“ 1280 = 0, which is the required representation of the problem mathematically.

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