Question 986321
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/22}}} in per hr
b: {{{b/14}}} in per hr
:
Find their lengths after 6 hrs
a: {{{(6a)/22}}} inches
b: {{{(6b)/14}}} inches
therefore when they are the same length
{{{(6a)/22}}} = {{{(6b)/14}}}
divide both sides by 6
{{{a/22}}} = {{{b/14}}}
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