请用AOPS的视频风格，以美国8年级学生能够理解的方式制作这个题目的讲解视频---**Question Stem:**
The one-way routes connecting towns A, M, C, X, Y, and Z are shown in the figure below (not drawn to scale). The distances in kilometers along each route are marked. Traveling along these routes, what is the shortest distance from A to Z in kilometers?
如图所示, A、M、C、X、Y、Z几座小镇之间通过单行道相连。图中标明了每条单行道的长度, 单位为千米。请问沿单行道从 A 行驶到 Z 的最短距离为多少 千米? (图形未按比例绘制)
**Chart/Diagram Description:**
Type: Directed graph (network diagram).
Main Elements:
- Nodes: Six nodes represented by circles labeled A, M, C, X, Y, and Z.
- Edges: Directed lines (arrows) connecting the nodes, representing one-way routes. Each edge is labeled with a numerical weight representing distance in kilometers.
- Edges and Weights:
- A to X: 5
- A to M: 8
- X to M: 2
- X to Y: 10
- M to Y: 6
- M to C: 14
- Y to C: 5
- Y to Z: 17
- C to Z: 10
- M to Z: 25
- Layout: Nodes are arranged generally from left to right, starting with A on the left, X and Y in the upper/middle section, M in the lower/middle section, C to the right of M and Y, and Z on the far right.
**Options:**
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
视频信息
答案文本
视频字幕
Welcome to this shortest path problem! We have six towns connected by one-way roads. Each road has a specific distance marked in kilometers. Our goal is to find the shortest route from town A to town Z. Let's start by examining the network structure and understanding all possible connections.
Now let's systematically find all possible paths from A to Z. We'll start with the first path: A to X to M to Y to C to Z. Following this route, we travel 5 kilometers from A to X, then 2 kilometers from X to M, then 6 kilometers from M to Y, then 5 kilometers from Y to C, and finally 10 kilometers from C to Z. Adding these up: 5 plus 2 plus 6 plus 5 plus 10 equals 28 kilometers total.
Let's continue exploring more paths. Path 2 goes from A to X to Y to C to Z. This gives us 5 plus 10 plus 5 plus 10, which equals 30 kilometers. Path 3 takes us from A to M to Y to C to Z. This route totals 8 plus 6 plus 5 plus 10, which equals 29 kilometers. So far, our shortest path is still the first one at 28 kilometers.
Now let's check the remaining paths. Path 4 goes from A to X to M to Z, giving us 5 plus 2 plus 25, which equals 32 kilometers. Path 5 is the direct route from A to M to Z, totaling 8 plus 25, which equals 33 kilometers. Path 6 goes from A to X to Y to Z, giving us 5 plus 10 plus 17, which equals 32 kilometers. All of these paths are longer than our current shortest path of 28 kilometers.
Perfect! We've found all possible paths from A to Z. Comparing all the distances: 28, 30, 29, 32, 33, and 32 kilometers, the shortest path is clearly 28 kilometers. This corresponds to the route A to X to M to Y to C to Z. Therefore, the answer is A: 28 kilometers. This systematic approach of exploring all possible paths ensures we find the optimal solution to this shortest path problem.