Let's break down the problem step-by-step to understand which equation represents the remaining distance to the destination in terms of [tex]\( t \)[/tex], the time in hours since leaving the airport.
1. Total Distance:
The plane needs to travel a total distance of 825 miles.
2. Distance Covered in First Hour:
After one hour, the pilot announces that the plane is 495 miles away from the destination. This means the plane has covered:
[tex]\[
825 \text{ miles} - 495 \text{ miles} = 330 \text{ miles}
\][/tex]
So, in the first hour, the plane covers 330 miles.
3. Distance Covered in Another Hour:
After the second hour, the plane begins its half-hour descent for the final 165 miles. This means for the two hours before the descent, the plane covers:
[tex]\[
825 \text{ miles} - 165 \text{ miles} = 660 \text{ miles}
\][/tex]
Since this 660 miles is covered in 2 hours, the plane’s speed remains constant:
[tex]\[
\frac{660 \text{ miles}}{2 \text{ hours}} = 330 \text{ miles per hour}
\][/tex]
Thus, in each hour, the plane covers 330 miles.
4. Equation for Remaining Distance:
To find an equation for the remaining distance, [tex]\( d \)[/tex], in terms of [tex]\( t \)[/tex], the time in hours since leaving the airport, note that every hour the plane travels 330 miles. Therefore, after [tex]\( t \)[/tex] hours:
[tex]\[
\text{Distance Covered} = 330t \text{ miles}
\][/tex]
Thus, the remaining distance to the destination is:
[tex]\[
d = 825 \text{ miles} - 330t \text{ miles}
\][/tex]
Therefore, the equation that represents the remaining distance to the destination in terms of [tex]\( t \)[/tex] hours is:
[tex]\[
d = 825 - 330t
\][/tex]
Thus, the correct equation from the given options is:
[tex]\[
d = 825 - 330t
\][/tex]
