Problem 18 · 2025 Math Kangaroo
Medium
Ratios, Rates & Proportions
distance-speed-time
The two bookworms Linki and Rechti eat their way through a row of books. Linki starts from the left and Rechti from the right, both at the same time. Linki eats through a book cover in 3 days and through all the pages of a book in 2 days. Rechti eats through a book cover in 1 day and through all the pages of a book in 2 days. In which book (see illustration) do the two meet?
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Answer: B — B
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Hint 1 of 2
Give each worm a 'days to chew through' cost for a cover and for a set of pages, then send them toward each other.
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Hint 2 of 2
Add up the days each worm spends, layer by layer, until their totals show them reaching the same book.
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Approach: accumulate the days each worm needs until they meet
- Linki (from the left) needs 3 days per cover and 2 days per book of pages; Rechti (from the right) needs 1 day per cover and 2 days per book of pages.
- After 13 days Linki has chewed through book A entirely and reached the pages of book B \((3+2+3+3+2)\); in those same 13 days Rechti has chewed through E, D and C and into book B \((1+2+1+1+2+1+1+2+1+1)\).
- They meet inside book B, which is (B).
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