During Christmas, Sam's candle and Tommy's candle were placed on an altar. Sam's candle was 15 cm longer than Tommy's candle. Sam's candle and Tommy'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, Tommy's candle was burnt out while Sam's candle was burnt out at 1. Find the original height of each candle.
(a) Tommy's candle
(b) Sam's candle
|
Sam |
Tommy |
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 Sam's candle burning → 2.5 hours of Tommy's candle burning
10 hours of Sam's candle burning → 5 hours of Tommy's candle burning
Time taken for Tommy's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Tommy's candle burning → 15 cm
1 hour of Tommy's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Tommy's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Tommy's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Tommy's candle = 22.5 cm
(b)
Original height of Sam's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm