Two Candles: 20 cm and 15 cm
Read the puzzle
Two candles are lit at the same time and each burns down at a steady rate. Candle A is 20 cm tall and burns 4 cm per hour. Candle B is 15 cm tall and burns 1.5 cm per hour. After how many hours are they the same height?
After how many hours are they the same height?
How big is the gap at the start, and how fast does it close?
2 hours
After 2 h: A is 20 − 8 = 12 cm, B is 15 − 3 = 12 cm.
How to solve it
Work with the gap between the two candles.
At the start A is 20 − 15 = 5 cm taller.
Each hour A loses 4 cm and B loses 1.5 cm, so the gap closes by 4 − 1.5 = 2.5 cm per hour.
Closing 5 cm at 2.5 cm per hour takes 5 ÷ 2.5 = 2 hours.
Check: after 2 hours A is 20 − 4 × 2 = 12 cm and B is 15 − 1.5 × 2 = 12 cm. A would burn out only after 5 hours, so both are still lit.
The usual slip is adding the rates: 5 ÷ (4 + 1.5) is under 1 hour, and at that point A is still taller. Another is comparing burn-out times (5 hours for A, 10 for B), which answers a different question.
Takeaway: divide the starting gap by the difference in burn rates, then check both heights.
