During Christmas, Ivan's candle and Sean's candle were placed on an altar. Ivan's candle was 20 cm longer than Sean's candle. Ivan's candle and Sean'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, Sean's candle was burnt out while Ivan's candle was burnt out at 1. Find the original height of each candle.
(a) Sean's candle
(b) Ivan's candle
| |
Ivan |
Sean |
Comparing the heights
of candles |
20 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 Sean's candle burning
10 hours of Ivan's candle burning → 5 hours of Sean's candle burning
Time taken for Sean's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Sean's candle burning → 20 cm
1 hour of Sean's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Sean's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Sean's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Sean's candle = 17.5 cm
(b)
Original height of Ivan's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
