Question

A small pipe takes 24 minutes longer to fill a tank than it takes a large pipe. The two pipes together can fill the tank in 9 minutes. How long does it take each pipe alone to fill the tank?

Answer 1

I found `36min` for the small and `12min` for the large

Explanation:

Call `s` the carryng capacity in liters/minute of the small pipe and `l` of the large. You can write:
`s=x/t`
`l=x/(t-24)`
`s+l=x/9` where `x` is the capacity of the tank in liters.
Substituting the first 2 into the last:
`x/t+x/(t-24)=x/9` cancel the `x`s:
`1/t+1/(t-24)=1/9`
`(t-24+t)9=t(t-24)`
`18t-216=t^2-24t`
`t^2-42t+216=0`
Using the Quadratic Formula:
`t_1=6min` NO too small
`t_2=36min` YES