Question

(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.​

Answer 1

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Let us consider,

speed of train = x km/h

And

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

As per second situation, the speed of train = (x – 8) km/h

As given, the train will take 3 hours more 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

⇒ 3x^2 – 24x – 3840 = 0

⇒ x^2 – 8x – 1280 = 0

Hence, x^2 – 8x – 1280 = 0 is the required representation of the problem mathematically

Hope it's Helpful.....:)