Problem 19 · 2019 Math Kangaroo
Hard
Ratios, Rates & Proportions
ratio
Julius has two cylinder-shaped candles of different heights and diameters. The first candle burns down in 6 hours, the second in 8 hours. They both burn down evenly. He lights both candles at the same time, and after three hours they are both equally tall. What was the ratio of their original heights?
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Answer: C — 5 : 4
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Hint 1 of 2
After 3 hours each candle has burned a fraction of its own height.
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Hint 2 of 2
Set the two leftover heights equal and compare the originals.
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Approach: equal leftover heights give the ratio
- In 3 hours the 6-hour candle burns half its height, leaving 1/2; the 8-hour candle burns 3/8, leaving 5/8.
- Equal heights now: h1 × 1/2 = h2 × 5/8.
- So h1 : h2 = (5/8) : (1/2) = 5 : 4.
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