Question

Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.

Answer 1

Let x minutes be time taken by the larger pipe to fill the cistern then the smaller pipe taken (x + 5) minutes. These two pipes would fill `(1)/x` and `(1)/(x + 5)` of the cistern in a minute, respectively.
`(1)/x + (1)/(x + 5) = (9)/(100)`
⇒ 9x² - 155x - 500 = 0
⇒ 9x² + 25x - 180x - 500 = 0
⇒ x (9x + 25) -20 (9x + 25) = 0
⇒ (9x + 25) (x - 20) = 0
⇒ x - 20 = 0
and 9x + 25 = 0
x = 20
and  x = `-(25)/(9)` ...(negligible)
Hence the time taken by the pipes to fill the cistern in 20 minutes and 25 minutes.