Let's solve the problem step-by-step.
1. Determine the rates at which Ben and Kate write reports.
- Ben takes 2 days to write 5 reports, so his rate is:
[tex]\[
\text{Ben's rate} = \frac{5 \text{ reports}}{2 \text{ days}} = 2.5 \text{ reports per day}
\][/tex]
- Kate takes 3 days to write 5 reports, so her rate is:
[tex]\[
\text{Kate's rate} = \frac{5 \text{ reports}}{3 \text{ days}} \approx 1.6666666666666667 \text{ reports per day}
\][/tex]
2. Calculate the difference in their rates.
- Subtract Kate's rate from Ben's rate to find out how much greater Ben's rate is:
[tex]\[
\text{Difference in rates} = \text{Ben's rate} - \text{Kate's rate} = 2.5 - 1.6666666666666667 = 0.8333333333333333
\][/tex]
So, the difference in their rates, with Ben's rate being greater, is approximately 0.8333333333333333 reports per day.
