Kate went to the airport with her parents and her brother Nick. While they (кажется вы пропустили слово they, когда писали задание) were waiting at the airport, Nick remembered that he had something important to tell Kate. Her friend phoned just as they were leaving to ask what time Kate's flight left. Previously Kate's friend had thought that she wouldn't be all to get to the airport in the time but she turned up while Kate was saying goodbye to her parents. She finally went through passport control and everybody waved (насколько я поняла, то тут должно было быть wave, а не wake, опечатка (?)) goodbye.
