Q22 of 34 Page 1

A train covers a distance of 90 kms at a uniform speed. It would have taken 30 minutes less if the speed had been 15 km/hr more. Calculate the original duration of the journey.

Let the speed be 'x' km/h


Distance covered = 90 km


As,


Time taken by train to cover 90 km by speed 'x' hours


Time taken by train to cover 90 km by speed 'x + 15'


Given, it would have taken 30 minutes less i.e. hour





⇒ x2 + 15x - 2700 = 0


⇒ x2 + 60x - 45x - 2700 = 0


⇒ x(x + 60) - 45(x + 60) = 0


⇒ (x - 45)(x + 60) = 0


⇒ x = 45 or x = -60


But x = -60 is not possible, as speed can't be negative.


Therefore, original speed = x = 45 km/h


And time taken by train to cover distance with this speed


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