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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.
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