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aloeverahe · Feb 23, 2009, 04:47 AM

Two candles have different lengths and thicknesses. The longer one can burn for $m$ hours and the shorter one for $n$ hours. After $k$ hours of burning, where $k<m$ and $k<n$ , both candles are the same length. What fraction of the longer candle's length was the shorter candle's length? Give the answer in its simplest form in terms of $m, n$ and $k$ .

For this question, i know we have to use $x$ and $y$ , but it gets me confused because how do i put it as a equation?

Please if anyone can help...
Thanks

Perito · Feb 23, 2009, 05:29 AM

Let the length of the first candle be L1.
Let the length of the second candle be L2.

The rate of burning of the first candle is L1/m (per hour). L1 is the length of the candle (unknown).

The rate of burning of the second candle is L2/n. L2 is the length of the second candle (also unknown).

After k hours the length of candle 1 is (L1 - k * (L1/m)) and the length of candle2 is (L2 - k * (L2/n)). Note this is just the initial length minus the rate of burn times the time. After k hours, we are told that the lengths are equal, so

L1-k*(L1/m) = L2-k*(L2/n)

factor L1 and L2 from each side.

L1(1-k/m) = L2(1-k/n)

The problem asks for the ratio of the candle's lengths (the fraction).

So, solve for L1/L2.