Final answer:
The unknown in the problem with the hose's rate being 1/9 is most likely the time it takes for the smaller hose working alone to fill the pool.
Step-by-step explanation:
The unknown in the problem regarding the rate of the hose with the large diameter being 1/9 is not fully specified within the given text. In context, it seems that the question may be referring to one hose being able to fill something at a rate of 1/9 of the capacity per some unit of time. However, to answer the question of which unknown you are trying to find: Option B, the time it takes for the smaller hose working alone to fill the pool, is likely the correct choice as it is the only option that refers to one hose working alone which can be related to the given rate. The other options pertain to working together or parts of a job, whereas the rate given seems to be for one hose only.