# Re: Length of Time

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Posted by Brad Paul on October 30, 2002 at 18:31:31:

In Reply to: Length of Time posted by RD on October 30, 2002 at 17:47:44:

: Two candles are in a building. One is red and the other is blue. The candles are the same height, but the red is slightly thicker. The red burns out in 3 hours and the blue 2. After an amount of time the length of the red left unburned was twice that of the blue. A person who was in the building had a watch but it stopped, and there was no other clock in the building. How long was the person there?

How tall are the two candle? I don't know so let me call their height h.

What is the rate at which the red candle burns?

rred=h/tred

Where tred is the time it takes for the red candle to burn out.

What is the rate at which the blue candle burns?

rblue=h/tblue

Where tblue is the time it takes for the blue candle to burn out.

At some time t we note that:
"length of the red left unburned was twice that of the blue"

What is the height of the red candle after time t?

hred(t)=h-rred t

What is the height of the blue candle after time t?

hblue(t)=h-rblue t

Write an equation for what was seen:

2 hred(t)=hblue(t)

or

2(h-h/tred t)=(h-h/tblue t)

solve for t

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