Question 975772
Think of this as uniform rates, task completion or doing a job.  The agents doing the task of consuming provisions are the "men".


r, the consumption rate of 1 man.  Time unit is "weeks".  Unclear how to take the quantity and unit for the provisions being consumed


{{{1200r*15}}} would be the given described provisions for the 1200 men for 15 weeks.


The question uses two different quantities of men and time, but for the same quantity of provisions.  {{{Something+somethingElse=1200r*15}}}.  Those two terms or parts are these:


{{{highlight_green(1200r*5+(1200-200)r*t=1200r*15)}}}, and the new variable, {{{t}}}, is included for the time asked in the question.  If this equation makes sense to you, then solving and understanding the result should be no difficulty for you.


{{{1200*5+1000*t=1200*15}}}
{{{1000t=1200*15-1200*5}}}
{{{10t=12*15-12*5}}}
{{{10t=120}}}
{{{highlight(t=12)}}}