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