Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours.If both hoses are turned on at the same time, how long will it take the pool to fill?
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To determine how long it will take the pool to fill when both hoses are turned on at the same time, we need to find the combined filling rate of hoses A and B.
Hose A can fill the pool in 4 hours, which means it has a filling rate of 1/4 of the pool per hour.
Hose B can fill the pool in 2 hours, which means it has a filling rate of 1/2 of the pool per hour.
When both hoses are turned on simultaneously, their filling rates are additive. Therefore, the combined filling rate will be (1/4 + 1/2) of the pool per hour.
To add the fractions (1/4 + 1/2), we need a common denominator, which is 4. We can convert 1/2 to 2/4 as both fractions will have the same denominator.
Now we can add the two fractions:
1/4 + 2/4 = 3/4
So, when both hoses are turned on, they can fill 3/4 of the pool per hour.
To find the time it takes to fill the whole pool, we can divide 1 (the entire pool) by the combined filling rate of 3/4.
1 รท (3/4) = 4/3
Multiplying the fractions by the reciprocal, 4/3 is equivalent to 4/3 * 1/1, which equals 4.
Therefore, it will take 4 hours for both hoses A and B to fill the pool when turned on at the same time.