A straight fence is to be built using posts 6 inches wide separated by lengths of chain 5 feet long. The fence begins and ends with a post. Which of the following could be the total length of the fence in feet?

Introduction / Context:
This question involves a mix of geometry, units and simple algebra. It models a straight fence made of posts and chains, where each post contributes a fixed width and each chain contributes a fixed length between posts. We must determine which total length is achievable.

Given Data / Assumptions:

• Each post is 6 inches wide, which is 0.5 feet.
• Each length of chain between two posts is 5 feet long.
• The fence starts and ends with a post.
• We must decide which of 17, 18, 19 or 20 feet could be the total length.

Concept / Approach:
Let the number of posts be n. Because the fence starts and ends with a post, the number of chain segments will be n - 1. The total length L (in feet) is the sum of the widths of all posts plus the lengths of all chains. We can write a formula for L in terms of n, then test which of the given lengths fits that formula with n as a positive integer.

Step-by-Step Solution:
Step 1: Convert post width to feet. Each post is 6 inches wide, so width = 6 / 12 = 0.5 feet.Step 2: Let n be the number of posts. Then the total width contributed by posts is 0.5n feet.Step 3: Number of chain segments is n - 1. Each chain segment is 5 feet long, so total chain length is 5(n - 1) feet.Step 4: Total length L = 0.5n + 5(n - 1).Step 5: Simplify L: L = 0.5n + 5n - 5 = 5.5n - 5.Step 6: Now test each option to see whether it can be written in the form L = 5.5n - 5 for some integer n.Step 7: For L = 17, solve 5.5n - 5 = 17 ⇒ 5.5n = 22 ⇒ n = 22 / 5.5 = 4. This is an integer, so 17 feet is possible with 4 posts and 3 chain segments.Step 8: For L = 18, 5.5n - 5 = 18 ⇒ 5.5n = 23 ⇒ n = 23 / 5.5, not an integer.Step 9: For L = 19, 5.5n - 5 = 19 ⇒ 5.5n = 24 ⇒ n = 24 / 5.5, not an integer.Step 10: For L = 20, 5.5n - 5 = 20 ⇒ 5.5n = 25 ⇒ n = 25 / 5.5, not an integer.

Verification / Alternative check:
For L = 17 feet and n = 4 posts, compute directly: post length = 4 * 0.5 = 2 feet and chain length = 3 * 5 = 15 feet. Total = 2 + 15 = 17 feet, confirming that 17 feet is achievable.

Why Other Options Are Wrong:
18, 19 and 20 feet would require a non integer number of posts, which is physically impossible.Therefore these values cannot correspond to a fence constructed under the given rules.

Common Pitfalls:
Some learners mistakenly multiply the number of posts by 5 feet or confuse the width of posts and length of chains.Another common error is to forget that there is one fewer chain than posts.Clearly defining n, using the correct lengths and then solving the simple linear equation prevents these mistakes.

Final Answer:
The total fence length that is possible is 17 feet.