Q. 474.2( 9 Votes )

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer :

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

Time taken to cover 180 km =


New speed of train = x + 9 km/h


Time taken to cover 180 km =


According to the question






1620 = x2 + 9x


x2 + 9x – 1620 = 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 = 9 c = – 1620


= 1. – 1620 = – 1620


And either of their sum or difference = b


= 9


Thus the two terms are 45 and – 36


Difference = – 36 + 45 = 9


Product = – 36.45 = – 1620


x2 + 45x – 36x + 1620 = 0


x(x + 45) – 36(x + 45) = 0


(x + 45) (x – 36) = 0


x = – 45 or x = 36 (but x cannot be negative)


x = 36


Hence the usual speed of the train is 36 km/h


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