The challenge is to find a model for what is happening out there on the fields. One fact is that the grass grows while the cows are eating. Another is that the cows tread on the grass and that diminish the extent of the days. There may be other phenomena's as well but we have only two observation anyway so we decide ourselves for the "growing grass" model!
The result with this model is that it will take 48 days for a single cow to eat all the grass.
Assume now that the grass at the start would last for B "cowdays", and that the growth is b "cowdays per day". Then:
(1) B+3b=3*7 and
(2) B+8b=8*3
that gives the growth b=3/5 "cowdays per day"
and the starting food would be: B=24*4/5=96/5 = 19.2 "cowdays".
Now suppose a single cow can be eating for d days. Then:
(3) B+d*b=d*1 or
d=B/(1-b)=(96/5)/(2/5)=48 days
Last updated: 2001 - 10 -30 by Ingvar Jönsson