SOLUTION: Hi 2 candles A and B. Candle A of a larger diameter was placed on a table. Candle B of a smaller diameter was placed on a 6cm stand so tgat it has the same height as A. Both we

Question 1126342: Hi
2 candles A and B. Candle A of a larger diameter was placed on a table. Candle B of a smaller diameter was placed on a 6cm stand so tgat it has the same height as A.
Both were lit at 11.45. Candle A and B burnt down to a height marked H at 15.15 and 16.45 respectively. The rate of burning for each candle was constant throughout.
Upon reaching height H candle A took 7 hours to burn out while B took 8 hours. Find the original height of A.
thanks

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
use rate * time = distance
:
let r1 be the rate for candle A and r2 be the rate for candle B
:
both candles begin by buring a distance of x
:
time candle A takes to burn distance x is 14.75 - 11.45 = 3.5 hours
:
time candle B takes to burn distance x is 16.45 - 11.45 = 5 hours
:
then we have
:
r1 * 3.5 = x
r2 * 5 = x
:
r1 * 7 = H
r2 * 8 = H -6
:
using the above equations, we know
:
r1 = x/3.5 and r1 = H/7
r2 = x/5 and r2 = (H-6)/8
:
therefore
:
x/3.5 = H/7
7x = 3.5H
x = 3.5H/7
:
x/5 = (H-6)/8
8x = 5H -30
x = (5H -30)/8
:
3.5H/7 = (5H -30)/8
28H = 35H -210
7H = 210
H = 30
:
x = 3.5*30/7 = 15
:
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Original height of candle A = 30 +15 = 45 cm
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