# Two pipes running

Let the time taken by one pipe to fill the tank be x minutes

The time taken by other pipe to fill the tank = x + 5 minutes

Volume of tank be V

Volume of tank filled by one pipe in x minutes = V

Volume of tank filled by one pipe in 1 minutes = V/x

Volume of tank filled by one pipe in minutes = Volume of tank filled by other pipe in minutes = Volume of tank filled by one pipe in minutes + Volume of tank filled by other pipe in minutes = V    200x + 500 = 9x2 + 45x

9x2 – 155x – 500 = 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 = 9 b = – 155 c = – 500

= 9. 500 = – 4500

And either of their sum or difference = b

= – 155

Thus the two terms are – 180 and 25

Difference = – 180 + 25 = – 155

Product = – 180.25 = – 4500

9x2 – 180x + 25x – 500 = 0

9x(x – 20) + 25(x – 20) = 0

(x – 20) (9x + 25) = 0

(x – 20) = 0 (9x + 25) = 0

x = 20 or x = – 25/9

x = 20 (time cannot be negative fraction)

Hence one pipe fills the tank in 20 mins. and other pipe fills the cistern in (20 + 5) = 25 mins

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