Question 9731
Let x = the required number of hours of burning time required for the candles to reach the same height.

The height of the blue candle, after x hours of burning is:
 8"-x hrs(1/4 " per hr) = {{{8 - (x/4)}}}

The height of the yellow candle, after x hours of burning is:

12" - x hrs(1/2" per hr) = {{{12 - (x/2)}}}

We want to know the value of x (the number of hours) when these two heights are equal.

{{{8-(x/4) = 12-(x/2)}}} Simplify and solve for x. Change x/2 to 2x/4

{{{(32 - x)/4 = (48 -2x)/4}}} Multiply both sides by 4.

{{{32 - x = 48 - 2x}}}

{{{2x-x = 48-32}}}

{{{x = 16}}}

The two candles will be the same height after burning for 16 hours.

Check:

The height of the blue candle, after burning for 16 hours will be: 

8" - 16(1/4") = 8" - 4" = 4"

The height of the yellow candle, after burning for 16 hours will be:

12" - 16(1/2") = 12" - 8" = 4"