During Christmas, Vincent's candle and Cody's candle were placed on an altar. Vincent's candle was 4 cm longer than Cody's candle. Vincent's candle and Cody'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, Cody's candle was burnt out while Vincent's candle was burnt out at 1. Find the original height of each candle.
(a) Cody's candle
(b) Vincent's candle
| |
Vincent |
Cody |
Comparing the heights
of candles |
4 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 Vincent's candle burning → 2.5 hours of Cody's candle burning
10 hours of Vincent's candle burning → 5 hours of Cody's candle burning
Time taken for Cody's candle to burn 4 cm in height
= 5 - 3
= 2 h
2 hours of Cody's candle burning → 4 cm
1 hour of Cody's candle burning → 4 ÷ 2 = 2 cm
Total time taken for Cody's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Cody's candle burning
= 5.5 x 2
= 11 cm
Original height of Cody's candle = 11 cm
(b)
Original height of Vincent's candle
= 11 + 4
= 15 cm
Answer(s): (a) 11 cm; (b) 15 cm
