Problem 11 · 2021 Math Kangaroo
Stretch
Fractions, Decimals & Percents
proportion
Tom had ten sparklers of the same size. He lit the first one. When only a tenth of it remained, he lit the second one. When only a tenth of that remained, he lit the third one, and so on. Sparklers burn at the same speed along their entire length, and one sparkler burns in 2 minutes. How long did it take for all 10 sparklers to burn down?
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Answer: B — 18 min 12 sec
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Hint 1 of 2
Each sparkler except the last only burns until a tenth is left before the next is lit.
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Hint 2 of 2
Add nine 'nine-tenths of 2 minutes' burns plus one full burn.
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Approach: sum the partial burns plus one full burn
- A whole sparkler burns in 2 minutes; burning down to one tenth uses 9/10 of that, i.e. 1.8 minutes.
- Sparklers 1 through 9 each contribute 1.8 minutes before the next is lit: 9×1.8 = 16.2 minutes.
- The tenth sparkler burns completely: +2 minutes, total 18.2 minutes.
- That is 18 min 12 sec, choice (B).
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