Two candles, one of which was 2 cm longer than the other were lit for Halloween.
The longer and thinner one was lit at 4 P.M. and the shorter but fatter one 15 minutes later.
Each candle burned at a steady rate, and by 8 P.M. both were the same length. The thinner one finally burned out at midnight and the fatter one an hour later.
How long was each candle originally?
Let L be the initial length of the Fat candle, and F(t) is its length at time t.
Let S(t) be the length of the Skinny candle at time T.
Noon is time zero.
The fat candle goes from L to zero in 8.75 hours (4:15 to 1 AM), being zero at time = 13
The skinny candle goes from L+2 to zero in 8 hours (4pm to midnight) becoming zero at t = 12 midnight.
F(t) = (L/8.75)*(13-t)
S(t) = [(L+2)/(8)]*(12-t)
F(8) = S(8)
let t=8:
5*L/(35/4) = 4*(L+2)/8
(20/35)L = (L+2)/2
40L = 35L + 70
L = 14
So the initial lengths are 14 (fat one) and 16 (skinny one)
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Posted by Larry
on 2024-01-02 08:47:57 |
Algebra Solution
