There are two pipes in a water reservoir of your school. Two pipes together take `11(1)/(9)` minutes to fill the reservoir. If the two pipes are opened seperately, then one pipe would take 5 mintutes more time than the other pipe. Calculate the time taken to fill the reservoir seperately by each of the pipes.

Explanation

Let the first pipe can fill the reservoir seperately in x minutes.
`:.` the second pipe can fill the reservoir sepreately in (x+5) minutes. Two pipes together can fill the reservoir in 1 minute
`((1)/(x)+(1)/(x+5))"part"=(x+5+x)/(x(x+5))"part"=(2x+5)/(x^(2)+5x)` part of the reservoir.
So, the two pipes together can fill in the reservoir in 1 minute `(x^(2)+5)/(2x+5)` part of it.
As per question, `(x^(2)+5)/(2x+5)=11(1)/(9)`
or, `(x^(2)+5)/(2x+5)=(100)/(9)or,9x^(2)+45x=200x+500`
or, `9x^(2)-155x-500=0`
or, `9x^(2)-(180-25)x-500=0`
or, `9x^(2)-180x+25x-500=0`
or, `9x(x-20)+25(x-20)=0`
or, `(x-20)(9x+25)=0`
`:.` either `x-20=0" "or,9x+25=0`
`impliesx=20" "or,9x=-25`
`impliesx=20" "or,x=-(25)/(9)`
But the value of x can not be negative `:.xne-(25)/(9)" ":.x=20`
Hence the first pipe in 20 minutes and the second pipe in 25 minutes can fill in the reservoir seperately.