Final answer:
By setting up linear equations representing the height of each candle as it burns over time, we can solve for the number of hours it takes for both candles to become the same height. After solving the equations, we find that the candles will be the same height after 8 hours.
Step-by-step explanation:
Rylee is burning two candles of different initial heights, with each candle burning at a different constant rate.
To find out after how many hours the candles will be of the same height, we can set up a linear equation for each candle and then solve for the time at which both equations yield the same height.
Let h represent the height of the candles and t the time in hours.
The first candle starts at 9 cm and decreases by 0.5 cm/hour, so its height after a given time t can be represented as:
h = 9 - 0.5t
The second candle starts at 15 cm and decreases by 1.25 cm/hour, so its height after time t is:
h = 15 - 1.25t
To find the time when both candles are of equal height, we set the two equations equal to each other:
9 - 0.5t = 15 - 1.25t
Now we solve for t by adding 1.25t to both sides and subtracting 9 from both sides:
0.75t = 6
Divide both sides by 0.75 to find t:
t = 8 hours
The candles will be the same height after 8 hours.