To find the total number of flights that depart each week from the local airport, we proceed as follows:
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Calculate the number of flights per day:
- The airport operates for 18 hours per day.
- There are 30 minutes in each half-hour segment, meaning there are \( 2 \) flights per hour (one every 30 minutes).
- Therefore, in 18 hours, the total number of flights is: \[ 2 \text{ flights per hour} \times 18 \text{ hours} = 36 \text{ flights per day} \]
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Calculate the total number of flights per week:
- There are 7 days in a week, so the total number of flights in a week is: \[ 36 \text{ flights per day} \times 7 \text{ days} = 252 \text{ flights per week} \]
Thus, the total number of flights that depart from the airport each week is: \[ \boxed{252} \]