Two pipes running together can fill a tank in minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

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 = 9x^{2} + 45x

9x^{2} – 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

9x^{2} – 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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