Question 1037630
Rate, Time, JOB.  The basic rule RT=J, based on rate being  {{{J/T=R}}}, in {{{JOB/TIME}}} unit.


N children all working at individual rates R will work at a rate NR.


"Clean their school" is 1 whole job.  Put the attention of time on HOURS.  Figure the days later.


12 children working 8 hours a day can clean up their school in 5 days, 
{{{12r*8*5=1}}}.



then 8 children working 19 hours a day will clean the school in how many days.
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Let t be the number of HOURS.
{{{8r*t=1}}}


The system of equations using time t in hours is  {{{system(12r*8*5=1,8r*t=1)}}}.
Two expressions which are both equal to 1.
{{{12r*8*5=8rt}}}
{{{12*5=t}}}
{{{highlight(t=60)}}}------------60 hours.


Now finish the answer according to the specified  19 hours per day.

{{{60*hours*(1/19)(days/hour)}}}


{{{highlight(3&3/19)}}}, which is THREE days and maybe some either finishing for part of a day, or a bit of "overtime" during the last of the three days.