Problem 4 · 2018 Math Kangaroo
Easy
Ratios, Rates & Proportions
distance-speed-time
A garden is split into equally sized square-shaped lots. A fast snail and a slow snail crawl in different directions along the outside edge of the garden. Both start at the corner S. The slow snail crawls 1 m in one hour and the fast one crawls 2 m in one hour. At which marked point will the two snails meet for the first time?
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Answer: B — B
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Hint 1 of 2
The two snails together cover the whole boundary before they meet, so add their speeds.
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Hint 2 of 2
Find how far the faster snail has gone when their combined distance equals the perimeter, then step that far around from S.
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Approach: combined speed reaches the perimeter; locate the meeting point
- Going opposite ways around the edge, the snails meet when the distances they have walked add up to the full perimeter.
- Their combined speed is 1 + 2 = 3 m per hour, so the fast snail covers two-thirds of the boundary and the slow one a third.
- Marking off the fast snail's two-thirds of the boundary from S lands exactly at point B.
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