Math Problem Statement
Lisa says, "I think we should walk 6 blocks north and 5 blocks west to get to the store." Kara says, "No, I think it's shorter if we walk 3 blocks west, 4 blocks north, 2 blocks west, and then 2 more blocks north." Whose route is the shortest?
Solution
To solve this, let's break down each person's route and compare the total distance they walk.
Lisa's Route:
- Walk 6 blocks north and 5 blocks west.
- The total distance Lisa walks is:
Kara's Route:
- Walk 3 blocks west, 4 blocks north, 2 blocks west, and 2 more blocks north.
- The total distance Kara walks is:
Conclusion:
Both Lisa and Kara walk the same total distance: 11 blocks.
Thus, neither route is shorter—they both result in the same total distance of 11 blocks.
Would you like a detailed explanation of why their routes are the same? Here are some related questions:
- How can we use the Pythagorean theorem to calculate the straight-line distance between the start and end point?
- What if the routes took diagonal shortcuts—how would the distance change?
- How can grid distances be optimized for shortest routes?
- What would happen if the blocks were not of equal size—how would that affect the answer?
- What are some other real-world examples of comparing routes on a grid?
Tip: The shortest path between two points on a grid is always a straight line, but in a grid system, you can walk along the edges, so the shortest path is the sum of blocks.
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Math Problem Analysis
Mathematical Concepts
Distance Calculation
Grid Systems
Addition
Formulas
Total distance = sum of blocks in each direction
Theorems
Grid Distance Theorem
Suitable Grade Level
Grades 5-7
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