Two pipes running together can fill a cistern in minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.

Let one pipe fills a cistern in x mins.

Other pipe fills the cistern in (x + 3) mins.

Running together can fill a cistern in minutes = 40/13 mins

Part filled by one pipe in 1min =

Part filled by other pipe in 1min =

Part filled by both pipes Running together in 1min =

13x^{2} + 39x = 80x + 120

13x^{2} – 41x – 120 = 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 = 13 b = – 41 c = – 120

= 13. – 120 = – 1560

And either of their sum or difference = b

= – 41

Thus the two terms are – 65 and 24

Difference = – 65 + 24 = – 41

Product = – 65.24 = – 1560

13x^{2} – 65x + 24x – 120 = 0

13x(x – 5) + 24(x – 5) = 0

(x – 5) (13x + 24) = 0

(x – 5) = 0 (13x + 24) = 0

x = 5 or x = – 24/13

x = 5 (speed cannot be negative fraction)

Hence one pipe fills a cistern in 5 minutes and other pipe fills the cistern in (5 + 3) = 8 minutes.

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