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

Both candles will have the same height after 4 hours.

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]</p><p>[tex]-0.5t = -2`

Multiplying by (-1)

`0.5t = 2`

`t = (2)/(0.5)`

`t = 4`

Both candles will have the same height after 4 hours.