Suppose that Caroline is a diligent hard-working second-year college student. One Saturday, she decides to start the day by working through 300 practice problems to study for the computer science class. Using a table to track her progress throughout the day, she notices that as the hours pass, it takes her longer to solve the problems.

Time

Total Problems Solved

7:00 AM

0

8:00 AM

120

9:00 AM

210

10:00 AM

270

11:00 AM

300

Use the table to answer the following questions.

The marginal, or additional, gain from Bella’s first hour spent working, from 7:00 AM to 8:00 AM, isproblems.

To calculate the **marginal gain** in the number of problems solved during the first hour (from 7:00 AM to 8:00 AM), we look at the total number of problems solved at 8:00 AM and subtract the total number of problems solved at 7:00 AM.

From the table:

- **Problems solved at 8:00 AM** = 120
- **Problems solved at 7:00 AM** = 0

So, the marginal gain from 7:00 AM to 8:00 AM is:

\[
\text{Marginal gain} = 120 - 0 = 120 \text{ problems}
\]

### Answer: The marginal gain from Bella’s first hour spent working, from 7:00 AM to 8:00 AM, is **120 problems**.

Would you like further explanations or details?

Here are some additional questions for practice:

1. What is the marginal gain from 9:00 AM to 10:00 AM?
2. What is the total number of problems solved by 9:00 AM?
3. What is the average number of problems solved per hour by 11:00 AM?
4. How does Caroline’s productivity change over time?
5. If Caroline continued for another hour, how many problems might she solve based on this trend?

**Tip:** Marginal gains often decrease over time as fatigue sets in, so pacing yourself during long study sessions can help maintain productivity!

Learn how to calculate the marginal gain in problem solving during a study session, using Caroline's progress table. This example covers arithmetic and rate concepts, focusing on how productivity changes over time. Suitable for students in Grades 7-9.

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