| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
<<< CLT::ULTRIX$:[NOTES$LIBRARY]MATH.NOTE;1 >>>
-< Mathematics at DEC >-
================================================================================
Note 631.0 <><><> Grazing Oxen <><><> No replies
THEBUS::KOSTAS "Wisdom is the child of experience." 23 lines 17-DEC-1986 13:08
--------------------------------------------------------------------------------
Hello,
This problem appeared in Isaac Newton's Arithmetica Univeralis
about 1712, and became the subject of a fifty dollar prize in
New England more than a hundred years ago.
"If 12 oxen eat grass ( which is growing uniformly all the time )
on 3 and 1/3 acres in 4 weeks, and if 21 oxen eat the grass
on 10 acres in 9 weeks, how many oxen will it take to eat all
the grass on 24 acres in 18 weeks?"
Use the following notation:
F = amount of Feed required by one ox per week
B = amount of grass at the Beginning on an acre
G = amount of grass Growing per week per acre
Enjoy,
kgg
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 631.1 | ox, more on | VINO::JMUNZER | Tue Dec 30 1986 16:45 | 32 | |
> "If 12 oxen eat grass ( which is growing uniformly all the time )
> on 3 and 1/3 acres in 4 weeks, and if 21 oxen eat the grass
> on 10 acres in 9 weeks, how many oxen will it take to eat all
> the grass on 24 acres in 18 weeks?"
>
> Use the following notation:
>
> F = amount of Feed required by one ox per week
> B = amount of grass at the Beginning on an acre
> G = amount of grass Growing per week per acre
If O = # oxen
A = # acres
W = # weeks,
then eaten grass = beginning grass + newly grown grass
i.e. W * O * F = A * B + W * A * G
Move to two variables: x = B / F
y = G / F
W O = A x + W A y
Interpret .0: 48 = 3 1/3 x + 13 1/3 y
189 = 10 x + 90 y
Solve: x = 10.8 and y = .9
Answer: O = (A x + W A y) / W
= (24 * 10.8 + 18 * 24 * .9) / 18
= 36 oxen
John
| |||||
| 631.2 | yes | THEBUS::KOSTAS | Wisdom is the child of experience. | Tue Dec 30 1986 17:26 | 29 |
re. .-1
well done.
Now some more observations:
Without repeating the problem, we end up with two equations:
4 * (12) F = 10/3 * B + 10/3 * 4 G
9 * (21) F = 10 B + 10 (9G)
Multiplying the first equation by 63 and the second by 16 to
eliminate F we get
21 B + 84 G = 16 B + 144 G
and B = 12 G which means that the grass had been growing 12 weeks
before the oxen were turned in
Now substituting into one of the original equations gives
F = (210/189) G which means that an ox can eat all the grass
that grows on an acre in one and one-ninth
weeks. F = (10/9) G.
Enjoy,
-kgg
| |||||