Respuesta :
6 taps....10 h......400 m³
4 taps......x h....1000 m³ (2 tanks)(500m³)
The different magnitudes are related to the magnitude of the unknown,
considering in each relationship that the magnitudes that do not intervene they remain constant in it.
So:
6 taps.....10h
4 faucets.......x h
The LESS taps, the MORE hours it will take. Inverse proportionality.
[tex]\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{4}{6} \ \ (Reverse) }}[/tex]
400 m³......10h
1000 m³........xh
The MORE m³, the MORE hours will be needed. Direct proportionality.
[tex]\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{400}{1000} \ \ (Direct) }}[/tex]
Considering that, in general, none of the magnitudes remains
1 constant, it is verified that:
[tex]\boldsymbol{\sf{\dfrac{4}{100}=(\dfrac{4}{6})(\dfrac{400}{1000} ) }}[/tex]
From where
[tex]\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{(4)(400)}{(6)(1000)} }}[/tex]
[tex]\boldsymbol{\sf{x=\dfrac{(10)(6)(1000)}{(4)(400) }=\dfrac{6000}{1600}=\boxed{\boldsymbol{\sf{37.5}}} }}[/tex]
Answer: It will take 37.5 hours. That is: 37 hours and 30 minutes.✅
