Solution
The Patient Pasture
Show the problem again
A meadow starts with some quantity of grass and grows more at a constant rate every day. Every cow eats the same amount per day. Ten cows eat the meadow bare in exactly 24 days, and twenty cows do so in exactly 8 days (grass keeps growing while they eat). What is the largest number of cows the meadow can feed indefinitely without ever running out? Give an integer.
Worked solution
Measure grass in units of one cow-day. If the initial stock is G and the growth is g per day, then 10 × 24 = G + 24g and 20 × 8 = G + 8g. Subtracting gives 80 = 16g, so g = 5 and G = 120. A herd of c cows keeps the meadow alive forever exactly when it eats no more than the daily regrowth, c ≤ g. Hence the answer is **5**; the stock of 120 is irrelevant to the long-run question.
Source: Newton-style grass-and-cows problem, after the classic in Newton's Arithmetica Universalis; numbers and question chosen for AxiomIQ. Statement written for AxiomIQ.