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