Two candles have different lengths and thicknesses. The longer one can burn for hours and the shorter one for hours. After hours of burning, where and , 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 and .

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

Please if anyone can help...
Thanks

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.