Q. 484.4( 7 Votes )

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Answer :

Let the original speed of the train be x km/h

Time taken to cover 90 km =


New speed of train = x + 15 km/h


Time taken to cover 90 km =


According to the question






2700 = x2 + 15x


x2 + 15x – 2700 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 15 c = – 2700


= 1. – 2700 = – 2700


And either of their sum or difference = b


= 15


Thus the two terms are – 45 and 60


Difference = 60 – 45 = 15


Product = 60. – 45 = – 2700


x2 + 60x – 45x – 2700 = 0


x(x + 60) – 45(x + 60) = 0


(x + 60) (x – 45) = 0


x = – 60 or x = 45 (but x cannot be negative)


x = 45


Hence the original speed of the train is 45 km/h


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