Question

a twelve in candle and an 18 inch candle are lit at 6pm. The 12 inch candle burns 0.5 inches every hour. The 18 inch candle burns 2 inches every hour (it's a cheap candle). At what time will the two candles be the same height

Answer 1

Relation of 12 inch candle height h with time t hours is :

h = 12 - 0.5t

Also, for 18 inch candle :

h = 18 - 2t

Let, after x hours height is same.

So,

$12-0.5x = 18 - 2x\\\\1.5x = 6\\\\x=4\ hours$

So, after 4 hours height of the candles will be same.

Hence, this is the required solution.