This problem belongs to prealgebra, not to calculus. Let be the time in hours it takes pipe 2 to drain the pool, so
that is the time it takes pipe 1 to fill it up, and from here are the
relative work done by pipe 2 draining (resp. pipe 1 filling) in 1 hour.
When then we open up both pipes they drain the pool by a rate of -th of a pool every hour
and we're said it takes then 8 hours to empty the pool, so we get:
, as must be
positive, and thus indeed the time it takes to fill up the pool with pipe 1 alone is hours