During Christmas, Paul's candle and Glen's candle were placed on an altar. Paul's candle was 24 cm longer than Glen's candle. Paul's candle and Glen'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, Glen's candle was burnt out while Paul's candle was burnt out at 1. Find the original height of each candle.
(a) Glen's candle
(b) Paul's candle
|
Paul |
Glen |
Comparing the heights of candles |
24 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 Paul's candle burning → 2.5 hours of Glen's candle burning
10 hours of Paul's candle burning → 5 hours of Glen's candle burning
Time taken for Glen's candle to burn 24 cm in height
= 5 - 1
= 4 h
4 hours of Glen's candle burning → 24 cm
1 hour of Glen's candle burning → 24 ÷ 4 = 6 cm
Total time taken for Glen's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Glen's candle burning
= 3.5 x 6
= 21 cm
Original height of Glen's candle = 21 cm
(b)
Original height of Paul's candle
= 21 + 24
= 45 cm
Answer(s): (a) 21 cm; (b) 45 cm