During Christmas, Tom's candle and Caden's candle were placed on an altar. Tom's candle was 9 cm longer than Caden's candle. Tom's candle and Caden'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, Caden's candle was burnt out while Tom's candle was burnt out at 1. Find the original height of each candle.
(a) Caden's candle
(b) Tom's candle
| |
Tom |
Caden |
Comparing the heights
of candles |
9 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 Tom's candle burning → 2.5 hours of Caden's candle burning
10 hours of Tom's candle burning → 5 hours of Caden's candle burning
Time taken for Caden's candle to burn 9 cm in height
= 5 - 2
= 3 h
3 hours of Caden's candle burning → 9 cm
1 hour of Caden's candle burning → 9 ÷ 3 = 3 cm
Total time taken for Caden's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Caden's candle burning
= 4.5 x 3
= 13.5 cm
Original height of Caden's candle = 13.5 cm
(b)
Original height of Tom's candle
= 13.5 + 9
= 22.5 cm
Answer(s): (a) 13.5 cm; (b) 22.5 cm
