Question

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

Answer 1

Answer:

Both candles will have the same height after 4 hours.

Step-by-step explanation:

The equation for the amount of candle remaining can be given by the following equations:

$Q(t) = Q(0) - at$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and a is how much it decreases, in inches, per hour.

Red candle:

8 inches tall and burns at a rate of 7 divided by 10 inch per hour. This means that $Q(0) = 8, a = 7/10 = 0.7$. So

$Q_{r}(t) = 8 - 0.7t$

Blue candle:

6 inches tall and burns at a rate of 1 divided by 5 inch per hour. This means that $Q(0) = 6, a = 1/5 = 0.2$. So

$Q_{b}(t) = 6 - 0.2t$

After how many hours will both candles be the same height ?

This is t when

$Q_{r}(t) = Q_{b}(t)$

$8 - 0.7t = 6 - 0.2t$

$0.2t - 0.7t = 6 - 8[/yrc][tex]-0.5t = -2$

Multiplying by (-1)

$0.5t = 2$

$t = \frac{2}{0.5}$

$t = 4$

Both candles will have the same height after 4 hours.