228. Cow, Goat, and Goose. A certain farmer found out that his cow and goat eat the grass on the meadow in 45 days, the cow and goose in 60 days, and the goat and goose in 90 days. If he releases the cow, goat, and goose on the field at the same time, how many days will it take them to eat all the grass on the meadow?

Sir Isaac Newton once showed how to solve puzzles where the grass on the meadows does not stop growing. However, in our puzzle, for the sake of simplicity, we will assume that due to unfavorable weather conditions, the grass has stopped growing.
228. Since the cow and the goat eat \(\frac{1}{45}\), the cow and the goose \(\frac{1}{60}\), and the goat and the goose \(\frac{1}{90}\) of all the grass in a day, we easily find that the cow eats \(\frac{5}{360}\), the goat \(\frac{3}{360}\), and the goose \(\frac{1}{360}\) of all the grass in a day. Therefore, all together they eat \(\frac{9}{360}\) (or \(\frac{1}{40}\)) of all the grass in a day, so, since there will be no growth of grass, they will eat all the grass in 40 days.