Two Candles: 32 cm and 22 cm
Read the puzzle
Two candles are lit at the same time and each burns down at a steady rate. Candle A is 32 cm tall and burns 4 cm per hour. Candle B is 22 cm tall and burns 2 cm per hour. After how many hours are they the same height?
After how many hours are they the same height?
Find the gap at the start, then how much it closes each hour.
5 hours
After 5 h: A is 32 − 20 = 12 cm, B is 22 − 10 = 12 cm.
How to solve it
Track the gap between the candles.
At the start A is 32 − 22 = 10 cm taller.
Each hour A loses 4 cm and B loses 2 cm, so the gap shrinks by 4 − 2 = 2 cm per hour.
A 10 cm gap closing at 2 cm per hour needs 10 ÷ 2 = 5 hours.
Check: after 5 hours A is 32 − 4 × 5 = 12 cm and B is 22 − 2 × 5 = 12 cm. A would last 8 hours and B 11 hours, so both are still burning.
A common error is to add the rates, 10 ÷ (4 + 2), giving under 2 hours, when A is still clearly taller. Both candles shrink, so only the difference in their speeds closes the gap.
Takeaway: starting gap ÷ difference in burn rates gives the time, and plugging the time back in confirms it.
