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Two candles of equal length are lit simultaneously at 12:00 pm. Candle 1 has 6 hours of burn time before it completely melts away. Candle 2 has 9 hours of burn time before completely melting away. When will Candle #2 have 3 times as much wax remaining as Candle #1?(You must be within 1 minute to be considered correct)

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facundo3141592

By finding the equations for the length of the candles as a function of time, we will see that the answer is 3.27 hours.

When will Candle2 have 3 times as much wax remaining as Candle1?

Here we assume that:

Both candles have the same original length L, and both decrease a constant rate.

Candle 1 is consumed in 6 hours, so it is consumed at a rate of:

L/6h.

This means that after a time t in hours, the length of candle 1 is:

L₁(t) = L - (L/6h)*t

For candle 2, the rate is:

L/9h

And the function for the length of candle 2 is:

L₂(t) = L - (L/9h)*t

Now we want to find the value of t such that:

L₂(t) = 3*L₁(t)

So we just solve:

L - (L/9h)*t = 3*(L - (L/6h)*t)

L - (L/9h)*t = 3L - (L/2h)*t

(L/2h)*t -  (L/9h)*t = 3L - L = 2L

(5.5L/9h)*t = 2L

t = 2*(9h/5.5) = 3.27 h

After 3.27 hours, candle 2 will have 3 times the wax that candle 1 has.

If you want to learn more about linear functions:

https://brainly.com/question/4025726

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