During Christmas, Wesley's candle and John's candle were placed on an altar. Wesley's candle was 8 cm longer than John's candle. Wesley's candle and John'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, John's candle was burnt out while Wesley's candle was burnt out at 1. Find the original height of each candle.
(a) John's candle
(b) Wesley's candle
| |
Wesley |
John |
Comparing the heights
of candles |
8 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 Wesley's candle burning → 2.5 hours of John's candle burning
10 hours of Wesley's candle burning → 5 hours of John's candle burning
Time taken for John's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of John's candle burning → 8 cm
1 hour of John's candle burning → 8 ÷ 4 = 2 cm
Total time taken for John's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of John's candle burning
= 3.5 x 2
= 7 cm
Original height of John's candle = 7 cm
(b)
Original height of Wesley's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm
