The least common multiple of 9 and 6 is 18 so in 18 months she will replace the bulb for the 2nd time and the air filter for the 3rd time. It will be the first time they are replaced together.
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Can you take a picture of the story?
This culture sounds like an early 1900's, mid 1800's culture. Back then, people respected the elders in their communities, oftentimes going over for a chat or a cup of tea. The saying "respect thy elders" comes from that era.
If you are talking about a certain culture, like an African, American, European, etc., it would probably be an Asian culture. Asian children are taught at an early age to respect and mind all elders, including their older siblings.
If you are talking about religion...every religion tells the kids to respect their elders!
Answer: I will be in your territory for some time.
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