During Christmas, Oliver's candle and Ivan's candle were placed on an altar. Oliver's candle was 8 cm longer than Ivan's candle. Oliver's candle and Ivan'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, Ivan's candle was burnt out while Oliver's candle was burnt out at 1. Find the original height of each candle.
(a) Ivan's candle
(b) Oliver's candle
|
Oliver |
Ivan |
Comparing the heights of candles |
8 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 Oliver's candle burning → 2.5 hours of Ivan's candle burning
10 hours of Oliver's candle burning → 5 hours of Ivan's candle burning
Time taken for Ivan's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of Ivan's candle burning → 8 cm
1 hour of Ivan's candle burning → 8 ÷ 4 = 2 cm
Total time taken for Ivan's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Ivan's candle burning
= 3.5 x 2
= 7 cm
Original height of Ivan's candle = 7 cm
(b)
Original height of Oliver's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm