During Christmas, John's candle and Albert's candle were placed on an altar. John's candle was 12 cm longer than Albert's candle. John's candle and Albert'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, Albert's candle was burnt out while John's candle was burnt out at 1. Find the original height of each candle.
(a) Albert's candle
(b) John's candle
| |
John |
Albert |
Comparing the heights
of candles |
12 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 John's candle burning → 2.5 hours of Albert's candle burning
10 hours of John's candle burning → 5 hours of Albert's candle burning
Time taken for Albert's candle to burn 12 cm in height
= 5 - 1
= 4 h
4 hours of Albert's candle burning → 12 cm
1 hour of Albert's candle burning → 12 ÷ 4 = 3 cm
Total time taken for Albert's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Albert's candle burning
= 3.5 x 3
= 10.5 cm
Original height of Albert's candle = 10.5 cm
(b)
Original height of John's candle
= 10.5 + 12
= 22.5 cm
Answer(s): (a) 10.5 cm; (b) 22.5 cm
