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