Your friend Abbie is making a movie. She is filming a fancy dinner scene and she has two types of candles on the table. She wants to determine how long the candles will last.
She takes a picture, lights the candles, and then lets them burn for 1 hour. She then takes a second picture. You can assume that each candle burns at its own constant rate.
Candle Type A initial height = 20 cm
Candle Type B initial height = 10 cm

Candle Type A height after burning for 1 hour = 16 cm
Candle Type B height after burning for 1 hour = 9 cm

You will use this information to help Abbie think about the candles she might use for her film.
Candles A and B are lit at the same time. What will be the height, in cm, of each candle after 3 hours of burning?

To find the height of each candle after 3 hours of burning, we need to determine the burning rate of each candle and then apply it to the given time.

If the initial height of Candle A was 20 cm, and after 1 hour of burning it measured 16 cm, then its burning rate is:

[tex]\textsf{Candle A burning rate}=\sf \dfrac{20\;cm-16\;cm}{1\;hour}=4\;cm/h[/tex]

If the initial height of Candle B was 10 cm, and after 1 hour of burning it measured 9 cm, then its burning rate is:

[tex]\textsf{Candle B burning rate}=\sf \dfrac{10\;cm-9\;cm}{1\;hour}=1\;cm/h[/tex]

To calculate the heights of both candles after 3 hours of burning, subtract three times the burning rate of each candle from its initial height:

[tex]\begin{aligned}\textsf{Height of candle A after 3 hours}&=\sf 20\;cm-(3\;h \times 4\;cm/h)\\&=\sf20\;cm-12\;cm\\&=\sf8\;cm\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Height of candle B after 3 hours}&=\sf 10\;cm-(3\;h \times 1\;cm/h)\\&=\sf 10\;cm-3\;cm\\&=\sf 7\;cm\end{aligned}[/tex]

Therefore, after 3 hours of burning, Candle Type A will be 8 cm tall, and Candle Type B will be 7 cm tall.