Sebastian works 20 hours per week at his new job, which he spends at his office. During his first week, though, he spent 10 of his work hours doing outdoor team building activities.
Let w represent the number of weeks since starting the job and h represent the total number of hours worked in the office.

The problem provides that Sebastian works a total of 20 hours per week. In his first week, he spent 10 hours on outdoor activities, leaving 10 hours worked in the office.

Let's break this down:

1. **Week 1**: Sebastian works 10 hours in the office (since the other 10 were spent on outdoor activities).
2. **After Week 1**: Each subsequent week, he works the full 20 hours in the office, since the problem implies that the outdoor activities were specific to the first week.

### Expression for total hours worked in the office (h)
- In **week 1**, Sebastian works 10 hours in the office.
- For every other week (\( w \geq 2 \)), he works 20 hours in the office.

Thus, the total number of hours worked in the office \( h \) after \( w \) weeks is:

\[
h = 10 + 20(w - 1) = 10 + 20w - 20 = 20w - 10
\]

### Final Equation:
\[
h = 20w - 10
\]

This equation represents the total number of hours Sebastian works in the office after \( w \) weeks.

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Would you like further clarification on how this equation was derived?

Here are 5 related questions:
1. How would the equation change if Sebastian spent 15 hours outdoors in the first week?
2. If Sebastian works an additional 5 hours each week after Week 3, how would that affect the equation?
3. How many total hours in the office does Sebastian work after 5 weeks?
4. What is the difference in hours worked between the first and the second week?
5. How can this equation be modified if Sebastian alternates between working 20 hours in the office and doing 5 hours of outdoor activities every other week?

**Tip**: To find patterns in word problems, breaking down the situation into its weekly components often helps clarify the structure.

Sebastian works 20 hours per week at his new job, which he spends at his office. During his first week, though, he spent 10 of his work hours doing outdoor team-building activities. Let w represent the number of weeks since starting the job and h represent the total number of hours worked in the office.

Learn how to calculate the total number of hours Sebastian works in the office using the linear equation h = 20w - 10. This problem involves key algebra concepts and is suitable for students in Grades 6-8.

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