Question

Two candles start burning at the same time. One candle is 15 cm tall and burns at a rate of 5 cm every 6 hours. The other candle is 25cmtall and burns at a rate of 2 1/2 cm every hour. How tall will the candles be when they first burn down to the same height?

Answer 1

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.