To find out how much Barbara's brother owes her, let's take a step-by-step approach:
1. Identify the time periods for Barbara and her brother's usage:
- Barbara used the washer for 3 hours.
- Her brother returned it 7 hours after Barbara first rented it (so he used it for a total of [tex]\(7 - 3 = 4\)[/tex] hours).
2. Calculate Barbara's rental charge:
- For the first 4 hours, the rental rate is [tex]$2 per hour.
- Barbara used it for 3 hours:
\[
\text{Barbara's charge} = 3 \text{ hours} \times 2 \text{ dollars/hour} = 6 \text{ dollars}
\]
3. Calculate Barbara's brother's rental charge:
- Barbara's brother used it for 4 hours, falling into the second rate category from the piecewise function:
- For the first 4 hours, he needs to pay $[/tex]2 per hour.
- After the initial 4 hours, he falls into the next tier, where any extra hours up to 8 hours are charged differently:
- The second part of the function is [tex]$26 + $[/tex]5 per each extra hour after 4 hours:
[tex]\[
4 \text{ hours } \to 26 + 5 \times (4 - 4) = 26 + 0 = 26 \text{ dollars}
\][/tex]
4. Total rental charge to be paid:
- Add Barbara's charge and her brother's charge together:
[tex]\[
\text{Total charge} = 6 \text{ dollars} + 8 \text{ dollars} = 14 \text{ dollars}
\][/tex]
### Result:
Barbara's brother owes her [tex]$8.
(Note: Given the structured setup, this matches the total calculated charge from our detailed step-by-step solution. Therefore, the correct answer based on the rental function and their respective timing usages is $[/tex]14.)
