Alright, let's break down this problem step-by-step to find out how many cases Jerry hears per hour.
1. Total Number of Cases:
Jerry hears a total of 5 cases.
2. Total Time in Hours:
Jerry spends [tex]\(2 \frac{3}{8}\)[/tex] hours hearing these cases. We need to convert the mixed number [tex]\(2 \frac{3}{8}\)[/tex] into an improper fraction or a decimal for easier calculations:
- First, convert the fractional part [tex]\(\frac{3}{8}\)[/tex] into a decimal:
[tex]\[
\frac{3}{8} = 0.375
\][/tex]
- Add the fractional part to the whole number:
[tex]\[
2 + 0.375 = 2.375 \text{ hours}
\][/tex]
So, the total time taken is [tex]\(2.375\)[/tex] hours.
3. Calculate Cases Heard Per Hour:
To find the number of cases heard per hour, we use the formula:
[tex]\[
\text{Cases per hour} = \frac{\text{Total number of cases}}{\text{Total time in hours}}
\][/tex]
Plugging in the numbers we have:
[tex]\[
\text{Cases per hour} = \frac{5}{2.375} \approx 2.1052631578947367
\][/tex]
Hence, Jerry hears approximately [tex]\(2.1053\)[/tex] cases per hour, or more precisely, [tex]\(2.1052631578947367\)[/tex] cases per hour.
