To find out how many more hours Brigid needs to pick strawberries to reach her goal of 5 bushels, let’s follow the steps outlined below based on the given equation [tex]\( \frac{5}{8} h + 1 \frac{1}{2} = 5 \)[/tex]:
1. Convert the mixed number to an improper fraction:
Brigid has already picked [tex]\(1 \frac{1}{2}\)[/tex] bushels of strawberries. Let’s convert [tex]\(1 \frac{1}{2}\)[/tex] into an improper fraction:
[tex]\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
\][/tex]
2. Set up the equation:
We can plug this value into the equation [tex]\( \frac{5}{8} h + 1 \frac{1}{2} = 5 \)[/tex]. Rewriting [tex]\(1 \frac{1}{2}\)[/tex] as [tex]\( \frac{3}{2} \)[/tex], we get:
[tex]\[
\frac{5}{8} h + \frac{3}{2} = 5
\][/tex]
3. Isolate the variable [tex]\(h\)[/tex]:
First, subtract [tex]\( \frac{3}{2} \)[/tex] from both sides to isolate the term involving [tex]\(h\)[/tex]:
[tex]\[
\frac{5}{8} h = 5 - \frac{3}{2}
\][/tex]
4. Simplify the right-hand side:
To subtract these fractions, we need a common denominator. Convert 5 to a fraction with a denominator of 2:
[tex]\[
5 = \frac{10}{2}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{10}{2} - \frac{3}{2} = \frac{10 - 3}{2} = \frac{7}{2}
\][/tex]
So, the equation now is:
[tex]\[
\frac{5}{8} h = \frac{7}{2}
\][/tex]
5. Solve for [tex]\(h\)[/tex]:
We need to solve for [tex]\(h\)[/tex] by multiplying both sides of the equation by the reciprocal of [tex]\( \frac{5}{8} \)[/tex]:
[tex]\[
h = \frac{7}{2} \times \frac{8}{5} = \frac{7 \times 8}{2 \times 5} = \frac{56}{10} = 5.6
\][/tex]
Brigid needs to pick strawberries for another [tex]\(5.6\)[/tex] hours to reach her goal.
Therefore, the correct choice is:
[tex]\[
\boxed{5 \frac{3}{5} \text{ hours}}
\][/tex]
