Answer:
The two candles will be 10 cm tall when they first burn down to the same height.
Explanation:
The length of the 1st candle = 15 cm
the rate at which it burns = 5 cm every 6 hours
thus, every hour it will burn 5/6 or 0.83 cm
now, the length of the 2nd candle = 25 cm
every hour it burns 2.5 cm
let x be the number of hours that passed after the candles start burning
then, height of the 1st candle after x hours = 15 - 5x/6
and height of the 2nd candle after x hours = 25 - 2.5x
we need these two to be equal
thus, 15 - 5x/6 = 25 - 2.5x
25 - 15 = 2.5x - 5x/6
10 = 5x/2 - 5x/6
10 = 10x/6
x = 6
now, the height of candle 1 after 6 hours = 15 - 5 = 10 cm
height of the 2nd candle will also be 10 cm but let us cross-check,
25 - 2.5(6) = 10 cm
Thus, the two candles will be 10 cm tall when they first burn down to the same height.