Inverse Proportions
A pool will be filled with two hoses. The larger hose can fill it in 6 hours and the smaller hose can do it in 8 hours.
Let's calculate the fraction of the pool that both hoses fill in one hour.
Since the larger hose fills the pool in 6 hours, in one hour it fills 1/6 of the pool.
The smaller hose needs 8 hours to fill the pool, so in one hour it fills 1/8 of the pool.
Working together, the total fraction of the pool filled is:
[tex]\frac{1}{6}+\frac{1}{8}[/tex]
The LCM of the denominators is 24, thus the sum of the fractions is:
[tex]\frac{1}{6}+\frac{1}{8}=\frac{4}{24}+\frac{3}{24}=\frac{7}{24}[/tex]
That is the fraction of the pool filled by both hoses in one hour. In two hours it will be double:
[tex]2\cdot\frac{7}{24}=\frac{7}{12}[/tex]
We must select option D. 7/12
