During Christmas, Archie's candle and Jeremy's candle were placed on an altar. Archie's candle was 12 cm longer than Jeremy's candle. Archie's candle and Jeremy'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, Jeremy's candle was burnt out while Archie's candle was burnt out at 1. Find the original height of each candle.
(a) Jeremy's candle
(b) Archie's candle
| |
Archie |
Jeremy |
Comparing the heights
of candles |
12 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 Archie's candle burning → 2.5 hours of Jeremy's candle burning
10 hours of Archie's candle burning → 5 hours of Jeremy's candle burning
Time taken for Jeremy's candle to burn 12 cm in height
= 5 - 2
= 3 h
3 hours of Jeremy's candle burning → 12 cm
1 hour of Jeremy's candle burning → 12 ÷ 3 = 4 cm
Total time taken for Jeremy's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Jeremy's candle burning
= 4.5 x 4
= 18 cm
Original height of Jeremy's candle = 18 cm
(b)
Original height of Archie's candle
= 18 + 12
= 30 cm
Answer(s): (a) 18 cm; (b) 30 cm
