Question

A train travels a distance of 480 km at a uniform speed if the speed had been 8 km per hour less than it would have taken 3 hours more to cover the same distance find the speed of the train

Answer 1

Distance travelled by the train = 480 kmLet the speed of the train be x kmph Time taken for the journey = 480/x Given speed is decreased by 8 kmph Hence the new speed of train = (x – 8) kmph Time taken for the journey = 480/(x – 8)   1280 = x2 – 8x  x2– 8x – 1280 = 0 On solving we get x = 40Thus the speed of train is 40 kmph

Answer 2

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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.....:)