 |
| |
|
|
|
|
Solution to:
Green Green Grass
Some assumptions:
- The cow, the goat, and the goose eat grass with a constant speed
(amount per day): v1 for the cow, v2 for the goat, v3 for the goose.
- The grass grows with a constant amount per day (k).
- The amount of grass at the beginning is h.
There is given:
- When the cow and the goat graze on the field together, there is no grass left
after 45 days. Therefore, h-45×(v1+v2-k) = 0, so v1+v2-k = h/45 = 4×h/180.
- When the cow and the goose graze on the field together, there is no grass left
after 60 days. Therefore, h-60×(v1+v3-k) = 0, so v1+v3-k = h/60 = 3×h/180.
- When the cow grazes on the field alone, there is no grass left after 90 days.
Therefore, h-90×(v1-k) = 0, so v1-k = h/90 = 2×h/180.
- When the goat and the goose graze on the field together, there is also no grass
left after 90 days. Therefore, h-90×(v2+v3-k) = 0, so v2+v3-k = h/90 = 2×h/180.
From this follows:
v1 = 3 × h/180,
v2 = 2 × h/180,
v3 = 1 × h/180,
k = 1 × h/180.
Then holds for the time t that the three animals can graze together:
h-t×(v1+v2+v3-k) = 0, so
t = h/(v1+v2+v3-k) = h/(3×h/180+2×h/180+1×h/180-1×h/180) =
36. The three animals can graze together for 36 days.
 back to the puzzle
|
| |
|
|
Copyright © 1996-2010. RJE-productions. All rights reserved. No part of this website may be published, in any form or by any means, without the prior permission of the authors.
|
