During Christmas, Billy's candle and Rael's candle were placed on an altar. Billy's candle was 15 cm longer than Rael's candle. Billy's candle and Rael's candle were lit at 1.00 p.m. and 9.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Rael's candle was burnt out while Billy's candle was burnt out at 1. Find the original height of each candle.
(a) Rael's candle
(b) Billy's candle
| |
Billy |
Rael |
Comparing the heights
of candles |
15 cm more |
|
| 1 p.m. |
Lighted |
|
| 9 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
2 h |
| 11 p.m. |
Same height |
| 4 a.m. |
|
Burnt out |
| 1.30 a.m. |
Burnt out |
|
Remaining burning time
for each candle to burn out |
5 h |
2.5 h |
(a)
After reaching the same height, total remaining burning time for each candle to burn out:
5 hours of Billy's candle burning → 2.5 hours of Rael's candle burning
10 hours of Billy's candle burning → 5 hours of Rael's candle burning
Time taken for Rael's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Rael's candle burning → 15 cm
1 hour of Rael's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Rael's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Rael's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Rael's candle = 22.5 cm
(b)
Original height of Billy's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm
