A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?
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To find out how long it will take to fill the pool if both hoses are used, we can calculate the combined rate at which they fill the pool.
Let's denote the rate at which the smaller hose fills the pool as "R1" and the rate at which the larger hose fills the pool as "R2".
We know that the smaller hose can fill the pool in 7 days, so its rate can be calculated as 1 pool / 7 days = 1/7 pools per day (R1 = 1/7).
Similarly, the larger hose can fill the pool in 4 days, so its rate is calculated as 1 pool / 4 days = 1/4 pools per day (R2 = 1/4).
When both hoses are used together, their rates are added up. Therefore, the combined rate, R_total, is equal to R1 + R2.
R_total = (1/7) + (1/4)
= (4/28) + (7/28)
= 11/28 pools per day
Now, we can calculate how long it will take to fill the pool using the combined rate. Let's denote the number of days it takes to fill the pool when both hoses are used as "x".
R_total = 1 pool / x days
We can equate the two equations to find x:
11/28 = 1/x
To solve for x, we can cross-multiply:
11x = 28
x = 28/11
Therefore, it will take approximately 2.54 days to fill the pool if both hoses are used.