This is basic “interview algebra” – it is *not* a differential equations problem. I suspect the whole trick to this problem is making you *think* you are supposed to be setting up and solving a differential equation – so basically if you are getting asked a problem like this in an interview the interviewer is trying to see if you make things hard for yourself under pressure. Useful information to know for both parties.
Grass grows in a field at some rate r, where r is the units of grass grown per day. It is known that if 10 sheep are turned out in the field, the grass will be gone in 20 days. On the other hand, if 15 sheep are turned out in the field, the grass will be gone in 10 days. If 25 sheep are turned out in the field, when will the grass be gone? ( Another Microsoft question from http://vijay.techi.googlepages.com/puzzles).
So I ran across pretty much this exact same problem on pg 36 of Mathematical Recreations from 1907 and they attributed the problem to Isaac Newton.
