During Christmas, Ivan's candle and Cole's candle were placed on an altar. Ivan's candle was 8 cm longer than Cole's candle. Ivan's candle and Cole'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, Cole's candle was burnt out while Ivan's candle was burnt out at 1. Find the original height of each candle.
(a) Cole's candle
(b) Ivan's candle
| |
Ivan |
Cole |
Comparing the heights
of candles |
8 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 Ivan's candle burning → 2.5 hours of Cole's candle burning
10 hours of Ivan's candle burning → 5 hours of Cole's candle burning
Time taken for Cole's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of Cole's candle burning → 8 cm
1 hour of Cole's candle burning → 8 ÷ 4 = 2 cm
Total time taken for Cole's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Cole's candle burning
= 3.5 x 2
= 7 cm
Original height of Cole's candle = 7 cm
(b)
Original height of Ivan's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm
