Number - Plants / Hills per Acre

[Guest]

Two related problems:

A) A farmer has a crop to plant in an acre. He plans to use 3' 6" rows, 3 plants per hill, hills 3' 6" apart. Determine number of plants.

B) The same farmer plans to have a number of hills in 3' 6" rows, 3' 6" apart in an acre. Determine number of hills.


An acre contains:

43560 square feet

208.71 feet x 208.71 feet

4840 square yards


How do I proceed ?

[Guest]

You may explain..............
What are hills?
What are rows?
What are plants?
Can you have rows of hills or hills of rows or both?
Can you have rows of plants or hills of plants?
Are plants things that grow in rows or grow on hills in rows?
Are plants actually real plants or non existant but just instances of planting?
Can you have rows of plants growing in rows on hills in rows?
or Do you have rows of hills with a plant on a hill or plants in rows and the rows on a hill?
Does the farmer have just one row of plants on a hill the length of an acre?

[Guest]

"You may explain..............
What are hills? More than one plant in a group placed together
What are rows? The plants are in a straight line
What are plants? A small version of a grown type (ex.- a tomato plant is a smaller version of the grown tomato bush)
Can you have rows of hills or hills of rows or both? rows of hills
Can you have rows of plants or hills of plants? both
Are plants things that grow in rows or grow on hills in rows? both
Are plants actually real plants or non existant but just instances of planting? real plants
Can you have rows of plants growing in rows on hills in rows? yes
or Do you have rows of hills with a plant on a hill or plants in rows and the rows on a hill? yes
Does the farmer have just one row of plants on a hill the length of an acre? " According to the problem, the rows are 3' 6"



0

[Guest]

You may give an illustration....
To me a hill is a small mountain.......
A row is what my granny does when she likes to do knitting.....
A plant is a small leafy thing that needs to be kept watered
Acording to the sizes given there could be one row of plants 3ft 6 ins wide by 12445 feet long to make an acre

[Guest]

208.71 / 3.5 = 59.63 = 60 rows per side x 4 sides = 240 rows

How do I calculate number of rows for the total acre ?

[Guest]

Your question does not make any sense to me...........
Draw a picture..........

There is no shape of the acre mentioned

Can be one row 3ft 6 ins wide by 12445 feet long ??????
I don't know where the hills are ?????

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>>>>>up to 12445 feet

Does this look like a row of plants??????

Does it look like a row of hills???????

[Guest]

3 plants per hill xxx 3' 6" apart xxx 3' 6" xxx ....... row 3 ' 6 " in length

xxx " " " "

etc..........

Shape of acre - square or rectangular.

[Guest]

What is a hill.....If I take a bucket of soil and turn it upside down like a sandcastle, is that a hill.???... If then plant 3 snowdrops on top on the sandcastle (or soilcastle) and make a row of them 3ft 6ins long, is that a row of hills with plants on the hills.

Acre can be square or rectangle.????
square acre of sides 208 ft by 208 ft...????
rectangle acre can be 1 foot wide by 43560 feet long...??????

[Guest]

A hill contains more than a single plant - 2 or 3 grouped together.

"square acre of sides 208 ft by 208 ft...????" Yes - the number of 3' 6" rows that could fit in that area.


"rectangle acre can be 1 foot wide by 43560 feet long...??????" Try that also.

[Guest]

The Grand Olde Duke of York......He marched his troops up to the top of the Hill and marched them down again....
And when they were up they were up.....
And when they were down they were down......
And when they were only half way up......
They were neither up nor down......

So a hill can also be an incline on the side of a hill.......
So in effect a hill on a hill......
So plants on the side of the hill, halfway up, are they neither up nor down......
Are they considered plants on the hill or not onthe hill.....

[Guest]

I'm sorry for asking the question.

[Guest]

All you had to do was describe the problem you were asking.
How can you ask a question if you don't know what the question is......
You could have described it in english descriptive terms or mathematically as mathematical or algebriac expressions.

I simply asked "what a hill is"......???

Jack and Jill went up the to get a pail of water.......
Jack fell down and broke his crown, and Jill came tumbling after.............

This is an example of the most plants that can be planted in an acre keeping the distance between each plant or planting position 3 ft 6 ins apart in all directions............

For an Equilateral Triangular Acre of land and,
Plants planted at corners of equilateral triangles having sides of 3 ft 6 ins.
This is the equivalent of plants planted 3ft 6 ins apart in rows 3 ft 6ins apart.
in all directions.

Area of plot = 0.5 x a x b x sin of the angle

43560 = 0.5 x a x b x Sin 60

43560 / (0.5 x Sin 60) = a x b

100579.5 = a x b

a and b are equal so take sq root of 100579.5

gives length of side of plot = 317 feet

3 ft 6 ins apart, divide by 3.5, gives 90 plants in the rows at the outer edge

there will be 1 plant less in each successive row....arithmetic series.

So find the sum of 90 terms from 1 to 90 having a common difference of 1

Sum = (90/2)x(2x1 + 1(90-1))

Sum = (90/2)x(91) = 4095 plants

So... 4095 plants for 1 plant at each corner of equilateral triangle.

If each corner is considered a hill with 3 plants planted at each hill then the total plants
would be (3 x 4095) = 12285 plants

[Guest]

A hill is where the plants or seeds are placed in the ground in a group of 3 or more, then covered with dirt. When the plants or seeds mature into a grown plant, each group is called a hill.

Please show the calculations for a square or rectangular acre also - never mind. Sorry for the bother.

[Guest]

A square acre is 208 by 208 feet
So that is 59 rows with 59 in a row if to be 3 ft 6 ins apart on each row.....diagonally they will be further apart.
3481 plants if 1 plant at each hill or 10443 plants if 3 plants on each hill. and rows parallel to the sides

A rectangular acre can be any size as long as its length multiplied by its width equals 1 acre. so you need to be more specific.

[Guest]

Sorry...I think I mis-calculated the triangular acre posted earlier.....
Corrected as below......

For an Equilateral Triangular Acre of land and,
Plants planted at corners of equilateral triangles having sides of 3 ft 6 ins.
This is the equivalent of plants planted 3ft 6 ins apart in rows 3 ft 6ins apart.
in all directions.

Area of plot = 0.5 x a x b x sin of the angle

43560 = 0.5 x a x b x Sin 60

43560 / (0.5 x Sin 60) = a x b

100579.5 = a x b

a and b are equal so take sq root of 100579.5

gives length of side of plot = 317 feet

3 ft 6 ins apart, divide by 3.5, gives 90 spaces between plants in the row at the outer edge so 91 plants in outer rows.

There will be 1 plant less in each successive row....arithmetic series.

So find the sum of 91 terms from 1 to 91 having a common difference of 1

Sum = (91/2)x(2x1 + 1(91-1))

Sum = (91/2)x(92) = 4186 plants

So... 4186 plants for 1 plant at each corner of equilateral triangle.

If each corner is considered a hill with 3 plants planted at it then the total plants
would be (3 x 4186) = 12558 plants

[Guest]

Thanks. What would be the largest and smallest rectangular shape for the acre in which the rows would cover as much of the area as possible ?

[Guest]

Don't know what you mean by the question.......

Planting in equi triangle formation means all are in rows and are 3.5 ft. from nearest in 6 directions.
also gives the most dense planting.
A rectangle Acre that fits this formation will have sides of length "S" by "0.866S".

For 1 Acre...... S x 0.866S = 43560

So .... S = sqroot(43560/0.866) = 224.28 ...and 0.866 x 224.28 = 194.22 feet.

There will be 65 plants along length and 1 plant less on alternate rows
Giving 32 x 64 = 2048 ....plus.....33 x 65 = 2145

Giving 4193 plants all together if 1 plant planted at each hill.
If 3 plant planted then..... 12579 plants.

[Guest]

Thanks again.

[Guest]

Just a follow -up note: I found an answer in another article - 10,677 plants.

[Guest]

What is the question...........???
Either explain the question.........
OR show the question..........
OR show the working out of the answer
" I found an answer in another article - 10,677 plants".....what is the point of publishing just numbers