Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 45 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Let x be the time it takes for the smaller hose to fill the pool on its own.
Working alone, the larger hose fills 1/45 of the pool in 1 minute.
Working together, the larger hose and the smaller hose fill 1/30 of the pool in 1 minute.
Since the smaller hose fills 1/x of the pool in 1 minute and they fill 1/30 of the pool in 1 minute together, then 1/x + 1/45 = 1/30.
Multiplying both sides by 90x and simplifying the equation gives 2x + 2 = 3x.
Subtracting 2x from both sides gives 2 = x. Answer: \boxed{2}.