Two Candles: Twice as Tall
Read the puzzle
Two candles of the same height are lit together and burn at a steady rate. Candle A lasts 4 hours, then it is gone. Candle B lasts 6 hours, then it is gone. After how many hours is B twice as tall as A?
Two candles of the same height are lit together and burn at a steady rate. A lasts 4 hours, B lasts 6 hours. After how many hours is B twice as tall as A?
A loses a quarter of its height each hour, B loses a sixth.
3 hours
After 3 h, A has 1/4 left and B has 1/2 left: twice.
How to solve it
Pick a handy height. 12 cm works because it divides by both 4 and 6.
A burns away in 4 hours, so it loses 12 ÷ 4 = 3 cm per hour. B burns away in 6 hours, so it loses 12 ÷ 6 = 2 cm per hour.
After t hours A is 12 − 3t and B is 12 − 2t. Set B equal to twice A: 12 − 2t = 2 × (12 − 3t) = 24 − 6t. So 4t = 12 and t = 3.
Check: after 3 hours A is 12 − 9 = 3 cm (a quarter of its height) and B is 12 − 6 = 6 cm (half its height). 6 is twice 3.
A common guess is 2 hours, the difference between 6 and 4. At 2 hours A is 6 cm and B is 8 cm, which is not double.
Takeaway: give the candles a concrete height, turn the lifetimes into burn rates, and write one equation.
