Two Candles: 12 cm and 8 cm
Read the puzzle
Two candles are lit at the same time and each burns down at a steady rate. Candle A is 12 cm tall and burns 2 cm per hour. Candle B is 8 cm tall and burns 1 cm per hour. After how many hours are they the same height?
After how many hours are they the same height?
Find the gap between the candles, then how much it shrinks each hour.
4 hours
After 4 h: A is 12 − 8 = 4 cm, B is 8 − 4 = 4 cm.
How to solve it
Find the gap and how fast it closes.
At the start A is 12 − 8 = 4 cm taller than B.
Each hour A loses 2 cm and B loses 1 cm, so the gap shrinks by 2 − 1 = 1 cm per hour.
A 4 cm gap closing at 1 cm per hour takes 4 ÷ 1 = 4 hours.
Check: after 4 hours A is 12 − 2 × 4 = 4 cm and B is 8 − 1 × 4 = 4 cm. Both still burn, since A would last 6 hours and B 8 hours.
A common mistake is to add the rates instead of subtracting them: 4 ÷ (2 + 1) is about 1.3 hours, but then A is still taller. The candles burn in the same direction, so only the difference in speed closes the gap.
Takeaway: time to equal height = starting gap ÷ difference in burn rates.
