Final answer:
The rate of water consumption is -0.9 ounces per minute. Charlie will need approximately 3 minutes and 20 seconds to empty the cup with 3 ounces left. It would have taken about 17 minutes and 47 seconds to consume a full cup at this rate.
Step-by-step explanation:
To calculate the rate at which the amount of water in the cup is changing, you can use the following information
- Charlie starts with 12 ounces of water in the cup.
- After 10 minutes, there are 3 ounces left.
This means Charlie drank 12 - 3 = 9 ounces of water in 10 minutes. The rate of change is 9 ounces/10 minutes, which simplifies to 0.9 ounces per minute. The rate is a negative value because the amount of water is decreasing over time. So, the rate of change is -0.9 ounces/minute.
For part B, to find out how many more minutes it will take for the cup to be empty, use the rate of change calculated earlier:
- There are 3 ounces of water left in the cup.
- Charlie drinks at a rate of 0.9 ounces per minute.
Therefore, it will take 3 ounces ÷ 0.9 ounces/minute = 3.33 minutes, or approximately 3 minutes and 20 seconds for the cup to be empty.
For part C, to determine how many minutes before Charlie starts drinking the cup was full, again use the rate of change:
- Charlie needs to drink 16 ounces to empty a full cup.
- Charlie drinks at a rate of 0.9 ounces per minute.
So, it would have taken Charlie 16 ounces ÷ 0.9 ounces/minute = 17.78 minutes, or approximately 17 minutes and 47 seconds to consume a full cup.