During Christmas, Luke's candle and David's candle were placed on an altar. Luke's candle was 10 cm longer than David's candle. Luke's candle and David'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, David's candle was burnt out while Luke's candle was burnt out at 1. Find the original height of each candle.
(a) David's candle
(b) Luke's candle
| |
Luke |
David |
Comparing the heights
of candles |
10 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 Luke's candle burning → 2.5 hours of David's candle burning
10 hours of Luke's candle burning → 5 hours of David's candle burning
Time taken for David's candle to burn 10 cm in height
= 5 - 3
= 2 h
2 hours of David's candle burning → 10 cm
1 hour of David's candle burning → 10 ÷ 2 = 5 cm
Total time taken for David's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of David's candle burning
= 5.5 x 5
= 27.5 cm
Original height of David's candle = 27.5 cm
(b)
Original height of Luke's candle
= 27.5 + 10
= 37.5 cm
Answer(s): (a) 27.5 cm; (b) 37.5 cm
