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?

90 minutes

Step-by-step explanation:

Hey, there! This is a walking together question, let's walk through it together.

Firstly, we assign a value for the volume of the swimming pool. Let's say this is x m^3

While working together, their rate is x/30

Now, for the larger hose, it takes 45 minutes. The rate here is x/45. To find the rate at which the smaller hose takes, we simply subtract the rate of the larger hose from that of both while working together.

Mathematically this is x/30 - x/45 = 15x/1350

Now to calculate the time taken, we simply divide the volume by this rate and that is x divided by 15x/1350 or x * 1350/15x = 90 minutes