During Christmas, Peter's candle and Ivan's candle were placed on an altar. Peter's candle was 4 cm longer than Ivan's candle. Peter's candle and Ivan's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Ivan's candle was burnt out while Peter's candle was burnt out at 1. Find the original height of each candle.
(a) Ivan's candle
(b) Peter's candle
| |
Peter |
Ivan |
Comparing the heights
of candles |
4 cm more |
|
| 1 p.m. |
Lighted |
|
| 8 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
3 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 Peter's candle burning → 2.5 hours of Ivan's candle burning
10 hours of Peter's candle burning → 5 hours of Ivan's candle burning
Time taken for Ivan's candle to burn 4 cm in height
= 5 - 3
= 2 h
2 hours of Ivan's candle burning → 4 cm
1 hour of Ivan's candle burning → 4 ÷ 2 = 2 cm
Total time taken for Ivan's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Ivan's candle burning
= 5.5 x 2
= 11 cm
Original height of Ivan's candle = 11 cm
(b)
Original height of Peter's candle
= 11 + 4
= 15 cm
Answer(s): (a) 11 cm; (b) 15 cm
