To compare the water purification rates of Marisol's and Timothy's machines, we first need to determine the average rate of water purification for each machine.
### Step 1: Calculate the Average Rate for Marisol's Machine
From the table:
- At 2 hours, the machine has purified 12 ounces.
- At 3 hours, the machine has purified 18 ounces.
- At 5 hours, the machine has purified 30 ounces.
- At 8 hours, the machine has purified 48 ounces.
We calculate the rate of purification between each pair of consecutive time points.
1. From 2 to 3 hours:
[tex]\[
\text{Rate} = \frac{18 - 12}{3 - 2} = \frac{6}{1} = 6 \text{ ounces/hour}
\][/tex]
2. From 3 to 5 hours:
[tex]\[
\text{Rate} = \frac{30 - 18}{5 - 3} = \frac{12}{2} = 6 \text{ ounces/hour}
\][/tex]
3. From 5 to 8 hours:
[tex]\[
\text{Rate} = \frac{48 - 30}{8 - 5} = \frac{18}{3} = 6 \text{ ounces/hour}
\][/tex]
Since each rate calculation results in the same value, Marisol's machine purifies water at a consistent rate of 6 ounces per hour.
### Step 2: Calculate the Rate for Timothy's Machine
For Timothy's machine:
- 9 hours after pouring water in, the machine has purified 81 ounces.
So, the rate of purification is:
[tex]\[
\text{Rate} = \frac{81 \text{ ounces}}{9 \text{ hours}} = 9 \text{ ounces/hour}
\][/tex]
### Step 3: Compare the Rates
- Marisol's machine purifies water at a rate of 6 ounces per hour.
- Timothy's machine purifies water at a rate of 9 ounces per hour.
To compare the rates, we subtract Marisol's rate from Timothy's rate:
[tex]\[
\text{Difference} = 6 \text{ ounces/hour} - 9 \text{ ounces/hour} = -3 \text{ ounces/hour}
\][/tex]
This means Marisol's machine purifies water at a rate of 3 ounces per hour slower than Timothy's machine.
### Conclusion
The correct sentence that compares their machines is:
(B) Marisol's machine purifies water at a rate 3 ounces per hour slower than Timothy's machine.
