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

The heights are the same after 4 hours.

Explanation:

The red candle burns at a rate of 7/10 inches per hour. In t hours, (7/10)t inches have burned. The height of the candle after t hours is 8 - (7/10)t.

The blue candle burns at a rate of 1/5 inch per hour. In t hours, (1/5)t inches have burned. The height of the candle after t hours is 6 - (1/5)t.

You need to find the time, t, when their heights are equal.

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

Multiply both sides by 10 (the LCD).

80 - 7t = 60 - 2t

-5t = -20

t = 4

The heights are the same after 4 hours.