2 candles in a supermarket
In the supermarket we can buy two different types of candles.
· The first type is 20 𝑐𝑚 long when new and burns at a rate of 2.5 𝑚𝑚 per hour.
· The second type is 24.5 𝑐𝑚 long when new and burns at a rate of 4 𝑚𝑚 per hour. We shall use 𝑡 to denote the time in hours, ℎ1 the function that gives the height in 𝑚𝑚 of the first type of candles after 𝑡 hours and ℎ2 the function that gives the height in 𝑚𝑚 of the second type of candles after 𝑡 hours.
1. Find the formula for ℎ1 (𝑡) and for ℎ2 (𝑡)
2. How long will each candle last?
3. Draw the graph of ℎ1 and ℎ2 on the same set of axes. Don’t forget to explain how you did your drawing.
4. Suppose we light both candles at the same time. After how many hours will they have the same height? Justify.
5. If you want the candles to end at the same time, which candle would you light first, and how long after this would you light the second one?