Question

Two candles start burning at the same time. One candle is
\[15\,\text{cm}\] tall and burns at a rate of
\[5\,\text{cm}\] every
\[6\] hours. The other candle is
\[25\,\text{cm}\] tall and burns at a rate of

\[2\dfrac{1}{2}\,\text{cm}\] every hour.
How tall will the candles be when they first burn down to the same height?

Answer 1

Let t be hours after they start. Heights:
- Candle A: 15 − (5/6)t (cm),
- Candle B: 25 − 2.5t (cm).

Set equal: 15 − (5/6)t = 25 − 2.5t → (2.5 − 5/6)t = 10 → (5/3)t = 10 → t = 6 hours.

Height then: 15 − (5/6)·6 = 15 − 5 = 10 cm (also 25 − 2.5·6 = 10 cm).

So they are 10 cm tall.