To determine how much Barbara's brother owes her for the use of the pressure washer, we can analyze each step of the scenario using the given piecewise rental function:
1. Understand the rental function:
- For [tex]\( 0 < h \leq 4 \)[/tex], the rental cost is \[tex]$26.
- For \( 4 < h \leq 8 \), the rental cost is \( 26 + 5(h-4) \).
- For \( 8 < h \leq 24 \), the rental cost is \$[/tex]60.
2. Calculate Barbara's cost:
- Barbara used the washer for 3 hours. Since [tex]\( 3 \)[/tex] falls in the range [tex]\( 0 < h \leq 4 \)[/tex], the cost is \[tex]$26.
3. Calculate the total cost:
- Barbara's brother used the washer and it was returned 7 hours after Barbara rented it. Therefore, the total usage time was 7 hours.
- For \( 7 \) hours, which falls in the range \( 4 < h \leq 8 \):
\[
\text{Total cost} = 26 + 5(7-4) = 26 + 15 = 41 \text{ dollars}
\]
4. Calculate the amount her brother owes:
- The brother owes the additional cost incurred for using the washer after Barbara. The additional cost can be calculated as:
\[
\text{Brother owes} = \text{Total cost} - \text{Barbara's cost} = 41 - 26 = 15 \text{ dollars}
\]
Thus, Barbara's brother owes her \$[/tex]15.00. Therefore, the correct option is:
[tex]\[
\$15.00
\][/tex]
