Question

Trees are to be planted alongside a road that is 55 yards long. if the distance between every two trees should be at least 5 yards, what is the maximum number of trees that can be planted?

Answer 1

The maximum number of trees that can be planted alongside a 55-yard-long road, with a minimum distance of 5 yards between them, is 11 trees.

Step-by-step explanation:

The question involves calculating the maximum number of trees that can be planted alongside a 55-yard-long road, with the condition that each tree must be spaced at least 5 yards apart. First, we have to consider that if n trees are to be planted, there will be n - 1 spaces between the trees. Using this, the distance occupied by the trees and the spaces between them can be represented as (n - 1) * 5. However, we must also factor in the first tree, which does not require a preceding space. Thus, the total distance would be (n - 1) * 5 + 1. To find the maximum number of trees, we set this total distance equal to 55 yards and solve for n.

(n - 1) * 5 + 1 ≤ 55
5n - 5 + 1 ≤ 55
5n ≤ 59
n ≤ 59 / 5
n ≤ 11.8

We cannot plant a fraction of a tree, so we must round down to the nearest whole number. Therefore, the maximum number of trees that can be planted is 11 trees.