Problem 14 · 2021 Math Kangaroo
Medium
Algebra & Patterns
Arithmetic & Operations
substitutionoff-by-one
Costa is building a new fence in his garden. He uses 25 planks of wood, each of which are 30 cm long. He arranges these planks so that there is the same slight overlap between any two adjacent planks. The total length of Costa's new fence is 6.9 metres. What is the length, in centimetres, of the overlap between any pair of adjacent planks?
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Answer: B — 2.5
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Hint 1 of 2
With 25 planks there are 24 overlaps, all equal.
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Hint 2 of 2
Compare the total plank length to the actual fence length to find the overlap total.
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Approach: account for total length lost to overlaps
- Laid end to end the 25 planks would span 25·30 = 750 cm.
- The fence is only 690 cm, so 750 − 690 = 60 cm is lost to overlapping.
- There are 24 equal overlaps, so each is 60 ÷ 24 = 2.5 cm.
- So the answer is B.
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