During Christmas, Paul's candle and Ryan's candle were placed on an altar. Paul's candle was 24 cm longer than Ryan's candle. Paul's candle and Ryan'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, Ryan's candle was burnt out while Paul's candle was burnt out at 1. Find the original height of each candle.
(a) Ryan's candle
(b) Paul's candle
| |
Paul |
Ryan |
Comparing the heights
of candles |
24 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 Paul's candle burning → 2.5 hours of Ryan's candle burning
10 hours of Paul's candle burning → 5 hours of Ryan's candle burning
Time taken for Ryan's candle to burn 24 cm in height
= 5 - 1
= 4 h
4 hours of Ryan's candle burning → 24 cm
1 hour of Ryan's candle burning → 24 ÷ 4 = 6 cm
Total time taken for Ryan's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Ryan's candle burning
= 3.5 x 6
= 21 cm
Original height of Ryan's candle = 21 cm
(b)
Original height of Paul's candle
= 21 + 24
= 45 cm
Answer(s): (a) 21 cm; (b) 45 cm
