During Christmas, Tim's candle and Japheth's candle were placed on an altar. Tim's candle was 15 cm longer than Japheth's candle. Tim's candle and Japheth's candle were lit at 1.00 p.m. and 9.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Japheth's candle was burnt out while Tim's candle was burnt out at 1. Find the original height of each candle.
(a) Japheth's candle
(b) Tim's candle
| |
Tim |
Japheth |
Comparing the heights
of candles |
15 cm more |
|
| 1 p.m. |
Lighted |
|
| 9 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
2 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 Tim's candle burning → 2.5 hours of Japheth's candle burning
10 hours of Tim's candle burning → 5 hours of Japheth's candle burning
Time taken for Japheth's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Japheth's candle burning → 15 cm
1 hour of Japheth's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Japheth's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Japheth's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Japheth's candle = 22.5 cm
(b)
Original height of Tim's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm
