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