the cow

10 days if you mean the cow could eat a 1/4 of the remaining grass in 2 days.

approximately 26 days

Well...grass grows back, y'know.

I assumed the grass continues to grow until eaten.

"approximately 26 days"

Explain your answer please.

Not necessarily. Why is Whimsical grinning ear to ear at the bottom of his post? Cows browse, they don't tear up the grass by the roots. And they don't browse that close to the ground, either. After a herd of cows has passed over a pasture, there's plenty left for sheep. I think this is a trick riddle.

I may be wrong, but it was an assumption I made.

I did this in Excel by approximating the growth and consumption of the grass in 1/100ths of a day. I tweaked the numbers to make the three-day consumption 4/3 of the two-day consumption. My final answer was a bit more than 26 days.

If the grass continues to grow after being eaten:
G = initial volume of grass (whole field)
g = volume of grass growth per day (whole field)
c = volume of consumed grass per day

2 days:
(G + 2g) / 4 = 2c
or
(i) G + 2g = 8c

3 days:
(G + 3g) / 3 = 3c
or
(ii) G + 3g = 9c (b)

subtract (i) from (ii) to get:
g = c
which means that the growth rate matches the consumption rate; so the field will never be completely consumed (unless I'm wrong).

I have a feeling you're not wrong, markr.

And so the answer is NEVER.

ok, (x/4)+(x/3) = 5, so, 7x/12 = 5. Then, x = (12*5)/7 = 60/7 = 8 4/7 days

12 days

Exactly 12 days