Tree Planting Problems

(1) line both ends of the tree planting
At this point, the final total amount of tree planting as a system. Start at one end of a tree line, the system can be seen as the initial value is 1, the intervals after a tree will be planted. The total tree = 1 + total number of segments. In addition, the length = spacing in the rows X (total tree -1), spacing = length / (total tree -1), (spacing is the distance between adjacent two trees). Namely: tree length = line +1 ÷ spacing, line spacing = length × (tree -1), spacing = line length ÷ (tree -1).
(2) line of one end of the planting
At this point, the system of initial value of zero. Then the total tree = total number of segments. Total tree length = spacing in the rows X. Namely: tree length = ÷ line spacing, line spacing in the rows × length = tree spacing = line length ÷ tree.
(3) line located at both ends of the system are not planting
initial value is zero, do not plant trees because of the last end, so the total number of segments of total tree = -1. Length = spacing in the rows X (total tree -1). Namely: tree length = ÷ line spacing -1, line length = spacing × (tree +1), spacing = line length ÷ (tree +1).
(4) closed tree planting, the type of end to end length ÷
tree = line spacing, line spacing in the rows × length = tree spacing = line length ÷ tree.

few more examples below we look to help people familiar with the tree-planting problem solving method:

【Example 1】 in the circular flower bed around the tree planting, known circumference of 50 meters, If you plant a tree every 5 meters, then a total number of trees can be planted? ()
A.9 B.10 C.11 D.12
】 【answer and resolve this problem B is completely closed circle on the punctuation, the number of easy to think that a tube into a closed segment geometry, then, of which overlap the beginning and end, that is one less than the original point, before the point of the closed graph the number of species is the proportion of the score one more segments, such as ns-meter line, in each point s m a point, then a total of n +1 points, which is OK to shape graphic. In the solution of this type of question, as long as there is no closed note, and then the specific calculation is more simple. Was chosen B. 【Example 2】

in a freshwater lake surrounded by perimeter is 8,040 meters built into the embankment, embankments willow tree planted every 8 meters, and then in between two adjacent trees planted at intervals of 2 m peach tree, how much should be prepared to peach trees? ()
A.1005 B.3015 C.1010 D.3020
A. Analysis】 B planted willow 8040 / 8 = 1005 (trees), which is the embankment was divided into 1005 segments willow. Also at the dike between two adjacent willow tree, is divided into a period of 2 meters, is divided into: 8 / 2 = 4 (above).
between the two willow trees planted peach trees, the ends do not need to plant a peach tree, so, peach tree, the number of segments less than 1, that is, between adjacent two willow trees planted peach 4-1 = 3 (trees). Thus, in total for the whole plant peach trees on the embankment as: 3X1005 = 3015 (trees). Example 3】 【

a triangle, the edge of tree planting in three, three side lengths of 156 meters, 186 meters, 234 meters, the distance between the tree and the tree was 6 m, three a corner of a tree must be planted, and asked totaling the number of trees planted? ()
A. 93 B. 95 C. 96 D. 99
A. Analysis】 C trilateral triangle form a triangle to form a closed line, the total tree planting (156 +186 +234) / 6 = 96.

】 【Example 4 to the 2008 Beijing Olympic Games into the green Olympics, the country in strengthening environmental protection, afforestation. Plan a unit of two stadiums in the two leading the way (do not intersect) planted trees on both sides, is transported back to a group of trees, the length of a road known to be another way, more than twice the length of 6,000 meters, If a tree planted every 4 meters, the less 2754; if planted tree 5 meters intervals, the number 396, the total number of trees seedlings?
A.8500 B.12500 trees trees trees C.12596 trees D.13000 Analysis
A. There are two ways to set】 D x trees seedlings by planting trees between the number of equations based on the equal distance (x + 2754-4) × 4 = (x-396-4) × 5, solve for X = 13000. (Tree planting on both sides of the road because the 2, then the tree than the number of segments increase 2 × 2 = 4)

few more by the above example, we understand the basic characteristics of the problem tree planting, and planting some of the problem solving methods.