Width of Space - Partial Solution/Explanation

[Guest]

The distance between the centers of two consecutive posts in a fence is L feet and the posts are X inches wide. The N pickets are A inches wide equally spaced. Determine width of each space.

Partial solution provided with problem:

12L - X - NA / N + 1

Please explain. Thanks.

[Guest]

Please reply - thanks.

[Guest]

I dont know the question detail what are "pickets"
But I assume......
12L is the dist between centres converted to inches.
- X then take away X the width of the post, actually 2 half posts.
- NA then take away NxA which is the width accupied by N pickets .... that leaves the total of the spaces between the pickets between each pai of posts.
/ N + 1 there will be N + 1 spaces if a space at each end....so divide by N+1 to get the distance between each picket.

[Guest]

Thanks again.

"Pickets" are the slats (usually wooden or vinyl) that form the fence.

[Guest]

I have a follow-up problem related problem and questions:

In a row of rivets, the space between any consecutive pair of rivets is 2.5 inches. Calculate distance from the center of rivet A to rivet B.

A B
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 rivets

The solution states there are 14 spaces, each 2.5 inches wide. The distance AB is 14 x 2.5 = 35 inches.

My questions-
Why is the number of spaces 1 less than the number of rivets and in the picket problem 1 is added to the N pickets?
Is the reason the number of rivets are known and the number of pickets are N?

It appears to me the A and B rivets would be the posts and the rivets between are the pickets.

[Guest]

The diagram is incorrect - Rivet B is the 15th rivet. B moved when I submitted the problem.

[Guest]

If rivets A and B are as the posts then there are ony 13 rivets in the calculation similar to pickets, and 14 spaces that is one more that the rivets.

The pickets had a space at each end between the first post and first picket and between the last picket and the end post

With the rivets you started with a rivet and ended with a rivet and considered the 14 spaces between the 15 rivets.

[Guest]

I understand now - thanks.