Daily Math Puzzle: 2026-07-02
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2026-07-02
At the 'Wacky Whirlwind' ride, there's a circular platform with a radius of 5 meters. A smaller, circular safety zone is marked in the exact center of this platform, with a radius of 1 meter. A maintenance worker needs to walk a specific path: starting from a point on the *outer edge* of the main platform, straight to a point on the *outer edge* of the safety zone. From there, they walk straight across the *diameter* of the safety zone. Finally, from the other side of the safety zone, they walk straight to another point on the *outer edge* of the main platform. To ensure minimal effort, what is the *shortest possible total distance* the worker could walk for this entire path?
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Solution
10 meters — Let R be the radius of the main circular platform (R=5m) and r be the radius of the central safety zone (r=1m).
To achieve the *shortest possible total distance*, all three segments of the worker's path must be aligned along a single straight line that passes through the center of both circles.
1. **Segment 1 (Outer edge of main platform to outer edge of safety zone):** The shortest path from the outer edge of the main platform to the outer edge of the safety zone is along a radius. Its length is R - r = 5m - 1m = 4 meters.
2. **Segment 2 (Across the diameter of the safety zone):** The worker walks straight across the diameter of the safety zone. Its length is 2r = 2 * 1m = 2 meters.
3. **Segment 3 (Other side of safety zone to outer edge of main platform):** From the opposite side of the safety zone, the shortest path back to the outer edge of the main platform is also along the extended radius. Its length is R - r = 5m - 1m = 4 meters.
Adding these lengths together: Total shortest distance = (R - r) + 2r + (R - r) = 4m + 2m + 4m = 10 meters.
Notice that this expression simplifies to 2R, which is simply the diameter of the main circular platform (2 * 5m = 10m).
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