A 12 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.