Hello! This is a practice problem that I am having trouble with! I just want to know how to solve it, as I am stuck on this.
Question:
Abbey 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
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?
I do believe this may have to do with ratios... But I'm not 100% sure how to solve it. Any help is much appreciated! Thanks in advance!
A clearly burns at 4cm/hr
B burns at 1cm/hr
so, the models are
A: y = 20-4x
B: y = 10 - x
Now you can plug in any value for x to see the height at that time.
The only ratio is that A burns 4 times as fast as B
So, if you can figure out how much B has shrunk in any time period, A has burned 4 times that far.
Oobleck, you have saved me! Thank you so much! I really appreciate it!
To solve this problem, you can use the concept of ratios and proportions. Here's how you can proceed:
Step 1: Find the rate of burning for each candle type:
- For Candle Type A, the initial height is 20 cm, and the height after 1 hour is 16 cm. So, in 1 hour, Candle Type A burns 20 cm - 16 cm = 4 cm.
- For Candle Type B, the initial height is 10 cm, and the height after 1 hour is 9 cm. So, in 1 hour, Candle Type B burns 10 cm - 9 cm = 1 cm.
Step 2: Calculate the burning rate per hour for each candle type:
- For Candle Type A, the burning rate is 4 cm per hour (as determined in Step 1).
- For Candle Type B, the burning rate is 1 cm per hour (as determined in Step 1).
Step 3: Use the burning rates to find the height of each candle after 3 hours:
- For Candle Type A, multiply the burning rate (4 cm per hour) by 3 hours: 4 cm/hour * 3 hours = 12 cm. Subtract this from the initial height (20 cm - 12 cm) to find the new height after 3 hours.
- For Candle Type B, multiply the burning rate (1 cm per hour) by 3 hours: 1 cm/hour * 3 hours = 3 cm. Subtract this from the initial height (10 cm - 3 cm) to find the new height after 3 hours.
So, the height of Candle Type A after 3 hours would be (20 cm - 12 cm) = 8 cm, and the height of Candle Type B after 3 hours would be (10 cm - 3 cm) = 7 cm.
Therefore, after 3 hours of burning, Candle Type A would be 8 cm tall and Candle Type B would be 7 cm tall.