SOLUTION: two candles have differen lengths and different thickness. the longer one would last 22 hours, and the shorter one would last for 14 hours. both candles are lit simultaneously, and

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Question 986321: two candles have differen lengths and different thickness. the longer one would last 22 hours, and the shorter one would last for 14 hours. both candles are lit simultaneously, and after 6 hours both have the same length remaining . what was the ratio of their original lengths
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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two candles have different lengths and different thickness.
the longer one would last 22 hours, and the shorter one would last for 14 hours.
both candles are lit simultaneously, and after 6 hours both have the same length remaining.
:
let a = the length of the 22 hr candle
let b = the length of the 14 hr candle
:
Find their burn rates in in/hr
a: a%2F22 in per hr
b: b%2F14 in per hr
:
Find their lengths after 6 hrs
a: %286a%29%2F22 inches
b: %286b%29%2F14 inches
therefore when they are the same length
%286a%29%2F22 = %286b%29%2F14
divide both sides by 6
a%2F22 = b%2F14
Cross multiply
14a = 22b
7a = 11b
equality is maintained when a = 11 and b = 7
:
what was the ratio of their original lengths
a:b length ratio = 11:7