Problem 13 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardpath-tracing
The shortest way from Atown to Cetown is through Betown. Going back along this road from Cetown to Atown, we first find the signposts on the left side of the road. Further on we find the road signs on the right side of the road. How far is it from Betown to Atown?
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Answer: D — 4 km
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Hint 1 of 2
Each signpost shows its distance to the towns; the two posts seen on the return trip pin down where each post stands on the road.
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Hint 2 of 2
Use the readings that name a common town to fix the gaps between the towns, then read off Betown-to-Atown.
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Approach: place the two signposts on the road from their distance readings
- On the way back from Cetown the two posts give their distances to the towns, which fixes the position of each post along the straight road.
- Matching up the readings that share a town determines the spacing Atown–Betown–Cetown.
- Reading off that spacing, the distance from Betown to Atown is 4 km, choice D.
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