During Christmas, Henry's candle and Charlie's candle were placed on an altar. Henry's candle was 20 cm longer than Charlie's candle. Henry's candle and Charlie's candle were lit at 1.00 p.m. and 10.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Charlie's candle was burnt out while Henry's candle was burnt out at 1. Find the original height of each candle.
(a) Charlie's candle
(b) Henry's candle
| |
Henry |
Charlie |
Comparing the heights
of candles |
20 cm more |
|
| 1 p.m. |
Lighted |
|
| 10 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
1 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 Henry's candle burning → 2.5 hours of Charlie's candle burning
10 hours of Henry's candle burning → 5 hours of Charlie's candle burning
Time taken for Charlie's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Charlie's candle burning → 20 cm
1 hour of Charlie's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Charlie's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Charlie's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Charlie's candle = 17.5 cm
(b)
Original height of Henry's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
