Problem 15 · 2018 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
The map shows the round trip that Captain Bluebear sails. Three distances are given. He sails from island to island starting at Berg, and altogether he covers 100 km. The distance between Wüste and Wald equals the distance from Berg to Blume going past Vulkan. How big is the distance between Berg and Wald?
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Answer: D — 33 km
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Hint 1 of 2
Three legs are given (17, 15, 26) and the whole loop is 100 km.
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Hint 2 of 2
Use the clue that Wüste–Wald equals Berg–Blume via Vulkan to fill the missing leg, then subtract.
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Approach: find the unknown legs from the 100 km loop and the equal-distance clue
- The trip Berg–Vulkan–Blume–Wüste–Wald–Berg totals 100 km.
- Wüste–Wald (26) equals Berg–Vulkan (17) + Vulkan–Blume, so Vulkan–Blume = 9.
- Now 17 + 9 + 15 + 26 + (Wald–Berg) = 100, so Wald–Berg = 33 km.
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