During Christmas, Liam's candle and Howard's candle were placed on an altar. Liam's candle was 6 cm longer than Howard's candle. Liam's candle and Howard'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, Howard's candle was burnt out while Liam's candle was burnt out at 1. Find the original height of each candle.
(a) Howard's candle
(b) Liam's candle
| |
Liam |
Howard |
Comparing the heights
of candles |
6 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 Liam's candle burning → 2.5 hours of Howard's candle burning
10 hours of Liam's candle burning → 5 hours of Howard's candle burning
Time taken for Howard's candle to burn 6 cm in height
= 5 - 3
= 2 h
2 hours of Howard's candle burning → 6 cm
1 hour of Howard's candle burning → 6 ÷ 2 = 3 cm
Total time taken for Howard's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Howard's candle burning
= 5.5 x 3
= 16.5 cm
Original height of Howard's candle = 16.5 cm
(b)
Original height of Liam's candle
= 16.5 + 6
= 22.5 cm
Answer(s): (a) 16.5 cm; (b) 22.5 cm
