Let's solve this step-by-step.
The given scenario can be represented by the equation:
[tex]\[
\frac{5}{8} h + 1 \frac{1}{2} = 5
\][/tex]
First, let's simplify [tex]\(1 \frac{1}{2}\)[/tex]:
[tex]\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
\][/tex]
Now, the equation becomes:
[tex]\[
\frac{5}{8} h + \frac{3}{2} = 5
\][/tex]
Next, isolate [tex]\( h \)[/tex] by subtracting [tex]\(\frac{3}{2}\)[/tex] from both sides:
[tex]\[
\frac{5}{8} h = 5 - \frac{3}{2}
\][/tex]
To perform the subtraction, convert 5 to a fraction with a common denominator of 2:
[tex]\[
5 = \frac{10}{2}
\][/tex]
So,
[tex]\[
5 - \frac{3}{2} = \frac{10}{2} - \frac{3}{2} = \frac{7}{2}
\][/tex]
Now our equation is:
[tex]\[
\frac{5}{8} h = \frac{7}{2}
\][/tex]
To solve for [tex]\(h\)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{5}{8}\)[/tex], which is [tex]\(\frac{8}{5}\)[/tex]:
[tex]\[
h = \frac{7}{2} \times \frac{8}{5}
\][/tex]
Multiply the numerators and the denominators:
[tex]\[
h = \frac{7 \times 8}{2 \times 5} = \frac{56}{10} = 5.6
\][/tex]
Convert 5.6 into a mixed number:
[tex]\[
5.6 = 5 \frac{3}{5}
\][/tex]
Thus, we have:
- Brigid has 3.5 bushels remaining to pick.
- She needs 5.6 hours, which is [tex]\(5 \frac{3}{5} \)[/tex] hours.
Therefore, the correct answer is [tex]\( 5 \frac{3}{5} \)[/tex] hours, written as [tex]\(5 \frac{3}{5}\)[/tex]. This matches the option [tex]\(5 \frac{3}{5}\)[/tex].
So the answer is:
[tex]\[
\boxed{5 \frac{3}{5}}
\][/tex]
