It takes a smaller hose twice as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together 25 minutes to fill the pool. How long will it take the larger hose to fill the pool by itself?

Answer: it will take the larger hose 37.5 minutes to fill the pool.

Step-by-step explanation:

Let t represent the number of minutes it will take the larger hose to fill the pool by itself. It means that the rate at which larger hose fills the pool per minute is 1/t

It takes the smaller hose twice as long to fill the swimming pool as it does the larger hose. It means that the number of hours it takes smaller hose to fill the pool is 2t and it fills it alone, then the rate at which it fills the pool per minute is 1/2t

By working together, they would work simultaneously and their individual rates are additive. It takes both hoses working together 25 minutes to fill the pool. It means that the rate at which they fill the pool together per minute is 1/25. Therefore,

1/t + 1/2t = 1/25

3/2t = 1/25

Cross multiplying, it becomes

2t = 3 * 25 = 75

t = 75/2 = 37.5 minutes