A12 inch candle burns 0.5 inches every hour. an 18
inch candle burns 2 inches every hour. after how
many hours will the two candles be at the same height?

After 4 hours,  two candles be at the same height.

Step-by-step explanation:

Let us assume after burning for  m hours, both candles are same height.

Length of candle A =  12 inch

Burning rate  = 0. 5 inches per hour

So, the candle burned in m hours   = m x  (0.5) = 0.5 m inches

The height of candle left after m hours =  12 - 0.5 m

Length of candle B =  18 inch

Burning rate  = 2 inches per hour

So, the candle burned in m hours   = m x  (2) = 2m inches

The height of candle left after m hours =  18 - 2 m

According to question:

After m hours: Height of candle A  =     Height of  candle B

or, 12 - 0.5 m  =  18 - 2 m

⇒ 12 - 18 = -2m + 0.5 m

or. - 6 = -1.5 m

or, m = 6 / 1.5 = 4

or, m = 4

Hence, after 4 hours,  two candles be at the same height.