During Christmas, Paul's candle and Bryan's candle were placed on an altar. Paul's candle was 10 cm longer than Bryan's candle. Paul's candle and Bryan'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, Bryan's candle was burnt out while Paul's candle was burnt out at 1. Find the original height of each candle.
(a) Bryan's candle
(b) Paul's candle
| |
Paul |
Bryan |
Comparing the heights
of candles |
10 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 Paul's candle burning → 2.5 hours of Bryan's candle burning
10 hours of Paul's candle burning → 5 hours of Bryan's candle burning
Time taken for Bryan's candle to burn 10 cm in height
= 5 - 3
= 2 h
2 hours of Bryan's candle burning → 10 cm
1 hour of Bryan's candle burning → 10 ÷ 2 = 5 cm
Total time taken for Bryan's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Bryan's candle burning
= 5.5 x 5
= 27.5 cm
Original height of Bryan's candle = 27.5 cm
(b)
Original height of Paul's candle
= 27.5 + 10
= 37.5 cm
Answer(s): (a) 27.5 cm; (b) 37.5 cm
