Sure, let's work through the problem step-by-step.
1. Determine Maria's total exercise time:
Maria exercises for [tex]\(1 \frac{5}{6}\)[/tex] hours every Saturday. To work with this more easily, we'll convert it to an improper fraction and then to a decimal.
[tex]\[
1 \frac{5}{6} = 1 + \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{11}{6}
\][/tex]
Converting this to a decimal,
[tex]\[
\frac{11}{6} \approx 1.8333333333333335 \text{ hours}
\][/tex]
2. Determine the fraction of time spent running:
Maria runs for [tex]\(\frac{3}{4}\)[/tex] of her total exercise time. To find out how long that is, we need to multiply her total exercise time by [tex]\(\frac{3}{4}\)[/tex].
[tex]\[
\text{Running time} = 1.8333333333333335 \times \frac{3}{4}
\][/tex]
3. Perform the multiplication:
[tex]\[
1.8333333333333335 \times \frac{3}{4} = 1.375 \text{ hours}
\][/tex]
4. Convert the running time to a mixed number:
To present the running time in a way suitable for the multiple-choice answers:
[tex]\[
1.375 \text{ hours} = 1 + 0.375 \text{ hours} = 1 + \frac{3}{8} \text{ hours} = 1 \frac{3}{8} \text{ hours}
\][/tex]
Thus, Maria runs for [tex]\(1 \frac{3}{8}\)[/tex] hours each Saturday.
Therefore, the correct answer is:
C [tex]\(1 \frac{3}{8}\)[/tex].
