Distance - Plowing An Acre

[Guest]

A farmer plans to plow an acre for a crop. The furrows** he plows are 12 inches in width. Determine distance traveled in traveling the acre.

Check my calculations:

Acre - 208 feet x 208 feet

208 x 12 in. per ft. = 2496 in.

2496 x 2496 = 6230016 in.

6230016 / 63360 in. per mile = 98 miles

Where did I make the error(s) ?

** A furrow is a trench created by a plow used for planting.

[Guest]

Determine distance traveled in traveling the acre.

The statement should read - Determine distance traveled in plowing the acre. Sorry for the typo.

[Guest]

Why do you do all these calculation......
If you have given the question any thought surely you could explain what you are trying to do.
You worked out by some means or looked it up to find and square acre was 208 feet x 208 feet.
The question told you each furrow was 12 inches which is 1 foot in width.
Can you see there would be then be 208 furrows plowed (we spell it ploughed) across the field and each furrow would be 208 feet long.
Assume we are not considering any travelling for turning at the ends etc
Then the distance travelled would be 208 x 208 = 43264 feet = 43264/5280 = 8.2 miles
OR an acre is 43560 sq feet = 208.7 x 208.7 = 43560 feet travelled = 43560/5280 = 8.25 miles

[Guest]

"You worked out by some means or looked it up to find and square acre was 208 feet x 208 feet." I used the square acre dimensions from the previous acre problem.

"Can you see there would be then be 208 furrows plowed (we spell it ploughed) across the field and each furrow would be 208 feet long." Yes - I wasn't thinking.

I have always made a problem more difficult than it is.

If the acre was rectangular as in the previous problem, would the dimensions of the acre be calculated in a similar way ?

[Guest]

A square acre sides are simply all equal in length (feet) to the square root of the area (in sq feet) of an acre.
A rectangular acre can be any shape as long as the length x breadth = 1 acre. so there a infinite sizes.
But, yes, the distance travelled would still be the length of the furrow x how many furrows

[Guest]

Thanks again.

[Guest]

Each furrow is 12 inches or 1 foot wide so for every foot he travells he plows 1 sq foot.
There are 43560 sq feet in an acre so he travells 43560 feet to plow an acre.
43560 / 5280 = 8.25 miles travelled to plow an acre.

[Guest]

Thanks again.

A question:

I read that in the pamphlet also. Would that information be included to let the farmer know when he traveled the distance in a field he plowed an acre to be accurate or just general information ?

[Guest]

I don't know, I am not a farmer, just like fiddling and working with numbers........
I imagine it can be used for all sorts of statistics and research guidelines and reports into farming practices and efficiencies.
It has to be used within the tolerances of the calculation and for most purposes a good guideline is all that is needed.
Estimates of how far travelled, how long engine is running, how much fuel is used, how long does it take etc etc.....

[Guest]

Thanks again. The pamphlet listed different furrow widths and miles traveled in plowing an acre.

[Guest]

Ploughing an acre of land.....How far travelled.......

If we measure the width of the furrow "W" in feet, then every foot travelled will give the area "W" plowed in square feet.
Total dist. travelled in plowing an acre will be (43560 / W) feet.
So for say a furrow width W = 4 feet.....Dist. Travelled will be 43560/ 4 = 10890 feet to plow an acre.
In miles this is = 10890 / 5280 = 2.0625 miles.....a quarter of dist. in my last post because furrow is 4 times wider.

[Guest]

Again, thanks.