During Christmas, Charlie's candle and Wesley's candle were placed on an altar. Charlie's candle was 12 cm longer than Wesley's candle. Charlie's candle and Wesley'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, Wesley's candle was burnt out while Charlie's candle was burnt out at 1. Find the original height of each candle.
(a) Wesley's candle
(b) Charlie's candle
|
Charlie |
Wesley |
Comparing the heights of candles |
12 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 Charlie's candle burning → 2.5 hours of Wesley's candle burning
10 hours of Charlie's candle burning → 5 hours of Wesley's candle burning
Time taken for Wesley's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Wesley's candle burning → 12 cm
1 hour of Wesley's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Wesley's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Wesley's candle burning
= 5.5 x 6
= 33 cm
Original height of Wesley's candle = 33 cm
(b)
Original height of Charlie's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm