Final answer:
Alicia arrived at the restaurant at 5:10 PM.
Step-by-step explanation:
To determine what time Alicia arrived at the restaurant, we need to add the time she spent waiting in the restaurant lobby and eating dinner to the time it took her to drive home.
She spent 45 minutes waiting in the restaurant lobby and one and a half hours eating dinner, which is equal to 90 minutes.
Adding the waiting time, eating time, and driving time together: 45 minutes + 90 minutes + 20 minutes = 155 minutes.
Since 60 minutes is equal to 1 hour, we can divide 155 minutes by 60 to find the number of hours:
155 minutes ÷ 60 = 2 hours and 35 minutes.
Alicia arrived home at 7:45 PM, so if we subtract 2 hours and 35 minutes from 7:45 PM, we can find the time she arrived at the restaurant: 7:45 PM - 2 hours and 35 minutes = 5:10 PM.
Therefore, Alicia arrived at the restaurant at 5:10 PM.