During Christmas, Mark's candle and Reggie's candle were placed on an altar. Mark's candle was 6 cm longer than Reggie's candle. Mark's candle and Reggie's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Reggie's candle was burnt out while Mark's candle was burnt out at 1. Find the original height of each candle.
(a) Reggie's candle
(b) Mark's candle
| |
Mark |
Reggie |
Comparing the heights
of candles |
6 cm more |
|
| 1 p.m. |
Lighted |
|
| 8 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
3 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 Mark's candle burning → 2.5 hours of Reggie's candle burning
10 hours of Mark's candle burning → 5 hours of Reggie's candle burning
Time taken for Reggie's candle to burn 6 cm in height
= 5 - 3
= 2 h
2 hours of Reggie's candle burning → 6 cm
1 hour of Reggie's candle burning → 6 ÷ 2 = 3 cm
Total time taken for Reggie's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Reggie's candle burning
= 5.5 x 3
= 16.5 cm
Original height of Reggie's candle = 16.5 cm
(b)
Original height of Mark's candle
= 16.5 + 6
= 22.5 cm
Answer(s): (a) 16.5 cm; (b) 22.5 cm
