Question

✴✴✴✴ HOT QUESTION BUT SIMPLE✴✴☺☺ !!!

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A train travels 360 km with uniform Speed. The speed of the train is increased by 5 km/h,it takes 48 minutes less to cover the same distance.Find the initial speed of the train.

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Answer 1

Let the initial speed of the train = x km/hr.

Given Distance covered by the train = 360km.

We know that Time = Distance/Speed

= (360/x) ------- (1)

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Given that the speed of the train increased by 5 km/hr.

We know that Time = distance/speed

= (360/x + 5) ----- (2)

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Given that it takes 48 minutes less to cover the same distance.

= > (360/x) - (360/x + 5) = 48/60

= > 360((1/x) - (1/x + 5)) = 48/60 [48 minutes = 48/60 hours]

= > 360((x + 5 - x)/x(x + 5)) = 48/60

= > 360 * 5 * 60 = 48x(x + 5)

= > 108000 = 48x^2 + 240x

= > 48x^2 + 240x - 108000 = 0

= > 48(x^2 + 5x - 2250) = 0

= > x^2 + 5x - 2250 = 0

= > x^2 - 45x + 50x - 2250 = 0

= > x(x - 45) + 50(x - 45) = 0

= > (x + 50)(x - 45) = 0

= > x = 45,-50

Speed cannot be negative.

Therefore, the initial speed of the train = 45 km/hr.

Hope this helps!