Question

Seis grifos, tardan 10 horas en llenar un

Answer 1

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.

$\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{4}{6} \ \ (Reverse) }}$

400 m³......10h

1000 m³........xh

The MORE m³, the MORE hours will be needed. Direct proportionality.

$\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{400}{1000} \ \ (Direct) }}$

Considering that, in general, none of the magnitudes remains

1 constant, it is verified that:

$\boldsymbol{\sf{\dfrac{4}{100}=(\dfrac{4}{6})(\dfrac{400}{1000} ) }}$

From where

$\boldsymbol{\sf{\dfrac{10}{x}=\dfrac{(4)(400)}{(6)(1000)} }}$

$\boldsymbol{\sf{x=\dfrac{(10)(6)(1000)}{(4)(400) }=\dfrac{6000}{1600}=\boxed{\boldsymbol{\sf{37.5}}} }}$

Answer: It will take 37.5 hours. That is: 37 hours and 30 minutes.✅