Respuesta :
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:
[tex]Q(t) = Q(0) - at[/tex]
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 [tex]Q(0) = 8, a = 7/10 = 0.7[/tex]. So
[tex]Q_{r}(t) = 8 - 0.7t[/tex]
Blue candle:
6 inches tall and burns at a rate of 1 divided by 5 inch per hour. This means that [tex]Q(0) = 6, a = 1/5 = 0.2[/tex]. So
[tex]Q_{b}(t) = 6 - 0.2t[/tex]
After how many hours will both candles be the same height ?
This is t when
[tex]Q_{r}(t) = Q_{b}(t)[/tex]
[tex]8 - 0.7t = 6 - 0.2t[/tex]
[tex]0.2t - 0.7t = 6 - 8[/yrc]
[tex]-0.5t = -2[/tex]
Multiplying by (-1)
[tex]0.5t = 2[/tex]
[tex]t = \frac{2}{0.5}[/tex]
[tex]t = 4[/tex]
Both candles will have the same height after 4 hours.
