The figure below shows Una's route from her home to the library. The time marked on each section of the road is the time it takes her to walk via that section of the road. Can you... The figure below shows Una's route from her home to the library. The time marked on each section of the road is the time it takes her to walk via that section of the road. Can you help Una find out which route takes the shortest time? (Time: minute)
Understand the Problem
The question presents a diagram of possible routes from Una's home to the library, with the time taken to walk each segment marked. The goal is to find the route that takes the least amount of time. This involves calculating the total time for each possible route and comparing them.
Answer
The shortest route is Home -> B -> C -> E, which takes 9 minutes.
Answer for screen readers
The route that takes the shortest time is Home -> B -> C -> E, which takes 9 minutes.
Steps to Solve
- Identify all possible routes
Based on the diagram, Una can take the following routes from her home to the library:
- Route 1: Home -> A -> B -> C -> E
- Route 2: Home -> A -> B -> D -> E
- Route 3: Home -> B -> C -> E
- Route 4: Home -> B -> D -> E
- Calculate the total time for each route
Add the time taken for each segment of each route:
- Route 1: $3 + 7 + 3 + 4 = 17$ minutes
- Route 2: $3 + 7 + 5 + 3 = 18$ minutes
- Route 3: $2 + 3 + 4 = 9$ minutes
- Route 4: $2 + 5 + 3 = 10$ minutes
- Compare the total times
Compare the total times calculated in the previous step to find the shortest time:
- Route 1: 17 minutes
- Route 2: 18 minutes
- Route 3: 9 minutes
- Route 4: 10 minutes
- Identify the shortest route
The shortest time is 9 minutes, which corresponds to Route 3 (Home -> B -> C -> E).
The route that takes the shortest time is Home -> B -> C -> E, which takes 9 minutes.
More Information
This problem demonstrates a simple application of graph theory, where you find the shortest path between two points in a network.
Tips
A common mistake would be to miss one or more possible paths. Another mistake could be misreading the time taken on each path segment, leading to incorrect total times for each route. To avoid this, carefully examine the graph and double-check the values before summing.
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