a) Find the shortest route from Wukong's home to the library. (Time in minutes). b) Find the shortest route from Una's home to the library. (Time in minutes). c) What is the minimu... a) Find the shortest route from Wukong's home to the library. (Time in minutes). b) Find the shortest route from Una's home to the library. (Time in minutes). c) What is the minimum time needed to get from A to C in minutes? (Options: 6, 7)
Understand the Problem
The image presents three separate route optimization problems. The first two problems (Exploration 1a and 1b) ask you to find the shortest route between two points given a network of paths with associated times. The third problem (Practice 1a) asks for the minimum time to travel from point A to point C, selecting the fastest route from the given options.
Answer
Exploration 1(a): Wukong's home $\rightarrow$ A $\rightarrow$ B (11 minutes) Exploration 1(b): Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ E and Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ D $\rightarrow$ E (17 minutes) Practice 1(a): 3 minutes.
Answer for screen readers
Exploration 1(a): The route from Wukong's home $\rightarrow$ A $\rightarrow$ B takes the shortest time with 11 minutes. Exploration 1(b): Both routes Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ E and Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ D $\rightarrow$ E take the shortest time with 17 minutes. Practice 1(a): The minimum time needed to get from A to C is 3 minutes, so neither (A) 6 nor (B) 7 are correct.
Steps to Solve
- Exploration 1(a): Identify possible routes from Wukong's home to the library
There are two possible routes: - Route 1: Wukong's home $\rightarrow$ A $\rightarrow$ B - Route 2: Wukong's home $\rightarrow$ A $\rightarrow$ C $\rightarrow$ B
- Exploration 1(a): Calculate the time for each route
Route 1: $8 + 3 = 11$ minutes Route 2: $8 + 4 + 4 = 16$ minutes
- Exploration 1(a): Determine the shortest route
Comparing the times, Route 1 (11 minutes) is shorter than Route 2 (16 minutes).
- Exploration 1(b): Identify possible routes from Una's home to the library
There are three possible routes: - Route 1: Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ E - Route 2: Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ D $\rightarrow$ E - Route 3: Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ D $\rightarrow$ E
- Exploration 1(b): Calculate the time for each route
Route 1: $3 + 7 + 3 + 4 = 17$ minutes Route 2: $3 + 7 + 5 + 2 = 17$ minutes Route 3: $3 + 7 + 3 + 5 + 2 = 20$ minutes
- Exploration 1(b): Determine the shortest route
Comparing the times, Route 1 (17 minutes) and Route 2 (17 minutes) are both shorter than Route 3 (20 minutes). Therefore, both Route 1 and Route 2 are shortest
- Practice 1(a): Identify possible routes from A to C
There are two possible routes: - Route 1: A $\rightarrow$ B $\rightarrow$ C - Route 2: A $\rightarrow$ C
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Practice 1(a): Calculate the time for each route Route 1: $2 + 1 = 3$ minutes Route 2: $4$ minutes
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Practice 1(a): Determine the shortest route and choose the answer
Comparing the times, Route 1 (3 minutes) is shorter Route 2 (4 minutes).
Exploration 1(a): The route from Wukong's home $\rightarrow$ A $\rightarrow$ B takes the shortest time with 11 minutes. Exploration 1(b): Both routes Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ E and Una's home $\rightarrow$ A $\rightarrow$ B $\rightarrow$ D $\rightarrow$ E take the shortest time with 17 minutes. Practice 1(a): The minimum time needed to get from A to C is 3 minutes, so neither (A) 6 nor (B) 7 are correct.
More Information
Route optimization is a very common and useful application of math that helps us to determine the fastest or shortest path between locations given a set of constraints.
Tips
A common mistake would be to miss a possible route or miscalculate the total time for a route. To avoid this, carefully trace each route on the diagram and double-check the addition.
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