Along a straight yard that is 225 metres long, 26 trees are planted at equal distances in a single row with one tree positioned exactly at each end of the yard; what is the distance in metres between two consecutive trees?

Introduction / Context:
This problem checks understanding of equal spacing along a line segment. When objects such as trees or poles are placed at equal intervals between two endpoints, the number of gaps between them is one less than the number of objects. Many learners mistakenly divide the total distance by the number of objects instead of by the number of gaps. Here, we have 26 trees on a 225 metre yard, and we need the distance between consecutive trees.

Given Data / Assumptions:
- Length of the yard = 225 metres.
- Total number of trees planted = 26.
- Trees are in a straight line at equal spacing.
- One tree is at each end of the yard.
- Distance required is between any two consecutive trees.

Concept / Approach:
If there are N trees in a straight line with one at each end, the number of equal intervals or gaps between them is N − 1. The equal spacing is therefore total length divided by (N − 1). After finding the number of intervals, we perform a simple division to obtain the distance between adjacent trees.

Step-by-Step Solution:
Number of trees = 26. Number of gaps between trees = 26 − 1 = 25. Total length of yard = 225 metres. Distance between consecutive trees = total length / number of gaps. Distance = 225 / 25. 225 ÷ 25 = 9 metres. Therefore, adjacent trees are 9 metres apart.

Verification / Alternative check:
We can check by multiplying back. If the spacing is 9 metres and there are 25 gaps, the total distance is 25 * 9 = 225 metres, which matches the given yard length. This confirms that the spacing of 9 metres is correct.

Why Other Options Are Wrong:
Option 8 metres would yield a total length of 25 * 8 = 200 metres, which is too short.
Option 10 metres would give 25 * 10 = 250 metres, exceeding the actual yard length.
Option 11 metres would give 25 * 11 = 275 metres, which is much longer than 225 metres.

Common Pitfalls:
A common mistake is dividing 225 by 26 instead of 25, which ignores the fact that gaps between trees are one fewer than the number of trees. Another mistake is misunderstanding the phrase “one tree positioned at each end” and not accounting properly for the endpoints in the count.

Final Answer:
The distance between two consecutive trees is 9 metres.