During Christmas, Zeph's candle and Archie's candle were placed on an altar. Zeph's candle was 16 cm longer than Archie's candle. Zeph's candle and Archie'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, Archie's candle was burnt out while Zeph's candle was burnt out at 1. Find the original height of each candle.
(a) Archie's candle
(b) Zeph's candle
| |
Zeph |
Archie |
Comparing the heights
of candles |
16 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 Zeph's candle burning → 2.5 hours of Archie's candle burning
10 hours of Zeph's candle burning → 5 hours of Archie's candle burning
Time taken for Archie's candle to burn 16 cm in height
= 5 - 1
= 4 h
4 hours of Archie's candle burning → 16 cm
1 hour of Archie's candle burning → 16 ÷ 4 = 4 cm
Total time taken for Archie's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Archie's candle burning
= 3.5 x 4
= 14 cm
Original height of Archie's candle = 14 cm
(b)
Original height of Zeph's candle
= 14 + 16
= 30 cm
Answer(s): (a) 14 cm; (b) 30 cm
