SOLUTION: I would be so grateful if you could help me with the following math problem: You have two candles, one is blue and is 8 inches tall, the other is yellow and is 12 inches tall.

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Question 9731: I would be so grateful if you could help me with the following math problem:
You have two candles, one is blue and is 8 inches tall, the other is yellow and is 12 inches tall. The blue candle burns 1/4 inch every hour and the yellow candle burns 1/2 inch every hour. If they start burning at the same time, when will they be the same height?
Note: I know that the blue candle takes a total of 32 hours to burn out, and the yellow takes 24 hours. At first I attempted a (ratextime=distance) problem, but was unsuccessful ... please help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
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+-+%28x%2F4%29
The height of the yellow candle, after x hours of burning is:
12" - x hrs(1/2" per hr) = 12+-+%28x%2F2%29
We want to know the value of x (the number of hours) when these two heights are equal.
8-%28x%2F4%29+=+12-%28x%2F2%29 Simplify and solve for x. Change x/2 to 2x/4
%2832+-+x%29%2F4+=+%2848+-2x%29%2F4 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"