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