I must drive from Bloomington to Cleveland. Several paths are available (see Figure 4).
The Correct Answer and Explanation is:
To determine the shortest driving time from Bloomington to Cleveland, we need to analyze all possible routes in the network diagram (Figure 4) and calculate their total travel times.
Step-by-Step Route Analysis
- Route 1: Bloomington → Indianapolis → Gary → Toledo → Cleveland
- Bloomington to Indianapolis: 1 hour
- Indianapolis to Gary: 2 hours
- Gary to Toledo: 3 hours
- Toledo to Cleveland: 3 hours
- Total: 1 + 2 + 3 + 3 = 9 hours
- Route 2: Bloomington → Indianapolis → Dayton → Toledo → Cleveland
- Bloomington to Indianapolis: 1 hour
- Indianapolis to Dayton: 3 hours
- Dayton to Toledo: 1 hour
- Toledo to Cleveland: 3 hours
- Total: 1 + 3 + 1 + 3 = 8 hours
- Route 3: Bloomington → Indianapolis → Dayton → Columbus → Cleveland
- Bloomington to Indianapolis: 1 hour
- Indianapolis to Dayton: 3 hours
- Dayton to Columbus: 2 hours
- Columbus to Cleveland: 3 hours
- Total: 1 + 3 + 2 + 3 = 9 hours
- Route 4: Bloomington → Cincinnati → Dayton → Toledo → Cleveland
- Bloomington to Cincinnati: 3 hours
- Cincinnati to Dayton: 2 hours
- Dayton to Toledo: 1 hour
- Toledo to Cleveland: 3 hours
- Total: 3 + 2 + 1 + 3 = 9 hours
- Route 5: Bloomington → Cincinnati → Columbus → Cleveland
- Bloomington to Cincinnati: 3 hours
- Cincinnati to Columbus: 2.5 hours
- Columbus to Cleveland: 3 hours
- **Total: 3 + 2.5 + 3 = 8.5 hours
✅ Correct Answer: Route 2 (Bloomington → Indianapolis → Dayton → Toledo → Cleveland) = 8 hours
Explanation
To determine the fastest route from Bloomington to Cleveland, we examine all feasible paths using the travel times provided in the figure. The network includes several interconnected cities with specified driving durations between each. Our objective is to find the minimum total travel time from the starting point (Bloomington) to the destination (Cleveland).
First, we identify each route and calculate the cumulative time taken. Route 1, via Indianapolis and Gary, results in a total of 9 hours. Route 2, which passes through Indianapolis, Dayton, and Toledo, proves more efficient, totaling 8 hours. Although Route 3 also passes through Indianapolis and Dayton, detouring to Columbus increases the travel time to 9 hours. Route 4, via Cincinnati and Toledo, takes 9 hours as well.
Route 5 seems promising due to its fewer legs and more direct path through Cincinnati and Columbus. However, its total time amounts to 8.5 hours — slightly longer than Route 2. This reveals that despite being more direct in appearance, travel time efficiency depends on the sum of the individual segments.
Thus, Route 2 is the optimal path, totaling only 8 hours. This highlights the importance of evaluating all route combinations, as the shortest path in distance may not always equate to the shortest in time. By applying a logical comparison of all available paths, we confirm that the quickest route from Bloomington to Cleveland is via Indianapolis, Dayton, and Toledo.
