It takes a smaller hose 4 times 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?
Do not do any rounding.
Let the time it takes the larger hose to fill the pool be x minutes.
Since the larger hose is 4 times faster than the smaller hose, it would take the smaller hose 4x minutes to fill the pool by itself.
Using the formula: Work = Rate x Time
Let T represent the total time taken when both hoses work together, then:
1/x + 1/4x = 1/25
Multiplying through by 100x:
100 + 25 = 4x
125 = 4x
x = 31.25
Therefore, it would take the larger hose 31.25 minutes to fill the pool by itself.