Question

A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height?

Answer 1

4 hours

Explanation:

The height of the red candle in inches can be modeled by ...

h = 8 - (7/10)t

where t is the number of hours it burns.

Likewise, the height of the blue candle can be modeled by ...

h = 6 - (1/5)t

The heights of the two candles will be the same when one expression for height is equal to the other.

8 - (7/10)t = 6 - (1/5)t

2 = t(7/10 - 1/5) . . . . . . . . . add (7/10)t -6

2/(5/10) = t = 4 . . . . . . . . . divide by the coefficient of t