# The distance betw

Let the speed of Deccan Queen be x km/h

Speed of another train = (x – 20)km/h

According to the question   taking LCM  4800 = x2 – 20x cross multiplying

x2 – 20x – 4800 = 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 = – 20 c = – 4800

= 1. – 4800 = – 4800

And either of their sum or difference = b

= – 20

Thus the two terms are – 80 and 60

Difference = – 80 + 60 = – 20

Product = – 80.60 = – 4800

x2 – 80x + 60x – 4800 = 0

x(x – 80) + 60(x – 80) = 0

(x – 80) (x + 60) = 0

x = 80 or x = – 60 (but x cannot be negative)

Hence the speed of Deccan Queen is 80 km/hr

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