Should be an easy but conceptual problem

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To solve the problem, first determine the rate at which one person can paint houses. Ten people can paint 60 houses in 120 days, which means one person can paint 6 houses in the same time frame. To find out how many houses 5 people can paint in 60 days, calculate their combined output based on their individual rates. Since 5 people can paint 30 houses in 120 days, in 60 days they would complete half of that, resulting in 15 houses. This logical breakdown helps explain the problem clearly.
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Homework Statement



This is a question I once encountered with a window advertisement popup, but I think I can work out the answer but I don't know how to logically explain it to my kids.


10 people can paint 60 houses in 120 days. How many houses can 5 people paint in 60 days

Homework Equations



No, that's all

The Attempt at a Solution



What a seem-to-be easy problem is not easy. (for me at least)
 
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Think about how you could represent this problem using straight lines
 
kenny1999 said:
10 people can paint 60 houses in 120 days.
So 1 person can paint 6 houses in 120 days.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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