Question 1011510
Two hundred students CONSUME THE FOOD in 50 days; so 1 student consumes THE FOOD in {{{200*50*days=10000*days}}}.  The one-student rate is  {{{(1/1000)(FOOD/DAY)}}}.  This is the key to use.


Two parts make the job of CONSUME THE FOOD.
200 students for 20 days, and then {{{200-50=150}}} students for unknown t days.



Again, the job is CONSUME THE FOOD.
{{{200*(1/10000)*20+150(1/10000)*t=1}}}


{{{2/10+(15/1000)t=1}}}


{{{1/5+3t/200=1}}}


{{{40+3t=200}}}


{{{3t=160}}}


{{{t=160/3}}}
{{{highlight(t=54&1/3)}}}, which may mean, fifty-three days and one-third of a day.