# A train travels 1

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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