Problem 21 · 2022 Math Kangaroo
Stretch
Geometry & Measurement
perimetertotal-then-divide
Ahmed and Sara start at point A and walk in the directions shown, at the same speed. Ahmed walks around the square garden and Sara walks around the rectangular garden. How many rounds must Ahmed walk to meet Sara at point A again for the first time?
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Answer: C — 3
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Hint 1 of 3
Work out how far one lap is for each child by adding up the sides of their garden.
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Hint 2 of 3
Each child is back at A after 1 lap, 2 laps, 3 laps… so skip-count the total distance for each.
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Hint 3 of 3
Look for the first distance that shows up in both lists — that is when they meet at A.
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Approach: skip-count each child's distances until they match
- Ahmed's square garden is 5 + 5 + 5 + 5 = 20 m around; Sara's rectangle is 10 + 5 + 10 + 5 = 30 m around.
- Ahmed is back at A after 20, 40, 60… metres; Sara is back at A after 30, 60, 90… metres.
- The first distance in both lists is 60 m, so that is when they meet at A again.
- Ahmed has gone 60 ÷ 20 = 3 laps, so he walks 3 rounds (choice C).
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