Question
Plum trees are planted along a new road at equal intervals, including both ends.The distance between every tow trees is 14m.What is the length of the new road if 8 trees are planted in all?
Answers
GPT-4o mini
To determine the length of the new road with 8 trees planted at equal intervals of 14 meters, we need to consider the arrangement of the trees.
When planting trees at equal intervals:
- The first tree is at the starting point (position 0).
- The second tree is 14 meters from the first tree.
- The third tree is 14 meters from the second tree, and so on.
If there are \( n \) trees planted, the distance between the first and the last tree can be calculated using the formula for the spacing:
\[
\text{Length of the road} = \text{Distance between trees} \times (\text{Number of trees} - 1)
\]
Given:
- Distance between trees = 14 meters
- Number of trees = 8
We can substitute these values into the equation:
\[
\text{Length of the road} = 14 \, \text{m} \times (8 - 1) = 14 \, \text{m} \times 7 = 98 \, \text{m}
\]
Thus, the length of the new road is **98 meters**.
When planting trees at equal intervals:
- The first tree is at the starting point (position 0).
- The second tree is 14 meters from the first tree.
- The third tree is 14 meters from the second tree, and so on.
If there are \( n \) trees planted, the distance between the first and the last tree can be calculated using the formula for the spacing:
\[
\text{Length of the road} = \text{Distance between trees} \times (\text{Number of trees} - 1)
\]
Given:
- Distance between trees = 14 meters
- Number of trees = 8
We can substitute these values into the equation:
\[
\text{Length of the road} = 14 \, \text{m} \times (8 - 1) = 14 \, \text{m} \times 7 = 98 \, \text{m}
\]
Thus, the length of the new road is **98 meters**.