Seis grifos, tardan 10 horas en llenar un depósito de 400m^3 de capacidad. ¿Cuántas horas tardarán cuatro grifos en llenar 2 depósitos de 500m^3 cada uno?

Question

asked Jul 7, 2023 132k views

1 Answer

Sohnryang · Answer 1 · 2023-07-14T01:26:37+0000

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:

The LESS taps, the MORE hours it will take. Inverse proportionality.

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

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

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

Considering that, in general, none of the magnitudes remains

1 constant, it is verified that:

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

From where

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

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

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