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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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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Let us consider,
The speed of train = x km/h
And
Time taken to travel 480 km = 480/x km/hr
As per second condition, the speed of train = (x – 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 × Time = Distance
Therefore,
(x – 8)(480/(x + 3) = 480
⇒ 480 + 3x – 3840/x – 24 = 480
⇒ 3x – 3840/x = 24
⇒ 3x2 – 8x – 1280 = 0
Therefore, the speed of the train, satisfies the quadratic equation, 3x2 – 8x – 1280 = 0, which is the required representation of the problem mathematically.