you are planting apple trees in a field, they should be planted 20 ft apart. assuming the field is 220 meters X 400 meters. how many trees can you plant?

Question

agricultural math

Answer 1

In real agriculture, you would not plant a tree on the boundary line (Every read “Mending Fences” by Robert Frost?).  With a distance of 20 feet between trees, this means that the field is divided into a grid (like graph paper) with 20ft*20ft squares in rows and columns.

Ah, but 20 ft is 6.1 meters (actually, 6.096, but “apart” ignores the width of a tree, so let’s be practical)

A grid of 220 meters * 400 meters can have

              (220/6.1) * (400/6.1)    grid boxes on it    [now, truncate, don’t round]

                 36 * 65   grid boxes

                  2340 grid boxes

 

If, indeed, you move each grid box half-a-box up and half-a-box left, then you can plant

                       37 * 66 trees (but some are now on the boundary)

                         2442    (remember, as Robert Frost wrote, “Good fences make good neighbors.”)

 

Disclaimer:  If both measurements were meant to be the same, then calculate this differently.

 

Additional disclaimer:  Most questions on this Forum are easy math.  However, if you want to pack trees tighter (like how the U.S. flag went from 48 to 50 stars), you calculate "distance between" as circles and can put more trees in the field.  For a real agriculture problem, this may be appropriate -- but a tractor must now drive diagonally at harvest time or pruning time.

Answer 2