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.
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