Forever. The key is to figure out the growth rate

of the grass vs. the eating rate of a single cow.

As we know from the first condition, one cow in three days can finish grass grown on 1/3 of the total area.

Therefore, at the end of three days, 2 cows would have finished grass grown on 2/3 of the total area. What happends to the grass on the leftover - 1/3 of the total area during the 3 days? According to the second condition, it takes 2 cows another 3 days to finish. Therefore, the grass on the 1/3 area doubled during the three days. So we got the growth rate for the grass: they double every 3 days.

Now back to the final question. In three days 1 cow would finish eating grass grown on 1/3 of the area. What happends to the grass on the other 2/3 area? They double in 3 days! Compare to the starting day, the poor cow has even more grass to eat on the 3rd day. So it would never finish eating the grass.

One muggle