According to the question, the given data is as shown below:
A hose with a larger diameter working alone is [tex]9[/tex] hours
A hose with a smaller diameter working alone is [tex]18[/tex] hours
Now, the time taken by the larger hose to fill the pool is [tex]\frac{1}{9}[/tex]
Similarly, the time taken by the smaller hose to fill the pool is [tex]\frac{1}{18}[/tex]
When they are working together, the expression can be written as:
[tex]\frac{1}{9} +\frac{1}{18} =\frac{1}{a}[/tex]
[tex]\frac{1}{a} =\frac{27}{9X18} =\frac{1}{6}[/tex]
The total time taken by the two hoses to fill the swimming pool is [tex]6[/tex] hours.
To learn more about the time and work procedure from the given link:
https://brainly.com/question/17273444
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