On both sides of a straight road 1760 m long, trees are planted at equal intervals of 20 m, including trees at the ends on each side. What is the maximum total number of trees that can be planted?

Introduction / Context:Equally spaced placements along a segment are a classic “inclusive endpoints” counting problem. When the spacing is d along a segment of length L, the number of points on one side is (L / d) + 1, provided trees are placed at both ends. Since there are two sides of the road, double the per-side count for the total.

Given Data / Assumptions:

• Road length L = 1760 m.
• Spacing d = 20 m between consecutive trees.
• Trees are planted on both sides and at both ends on each side.

Concept / Approach:For one side, with trees at both endpoints, the count is N_side = (L / d) + 1. Then total trees = 2 * N_side, because the same pattern is repeated on the other side. The key is not to forget the extra “+1” that arises from including both endpoints.

Step-by-Step Solution:

Verification / Alternative check:Visualize marks every 20 m from 0 to 1760 on one side: positions 0, 20, …, 1760 (inclusive). Counting by step size confirms 89 positions per side, validating the formula.

Why Other Options Are Wrong:176 ignores one of the endpoints across both sides. 180 assumes an extra interval or double-counts. 174 and 172 are undercounts due to missing endpoints or misapplied spacing.

Common Pitfalls:Using only L / d without adding 1, or forgetting to multiply by 2 for both sides of the road.

Final Answer:178