# The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two trains differ by 20 km/hr.

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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