Tom was off to the airport for his first-ever overseas holiday. After his taxi had gone 10 Km, he realized he had left his passport on the kitchen table at his mother's house. He got the the taxi to stop at a telephone booth, where he called his mother asking her to bring his passport to the airport. His mother hurriedly got into her car and took off after the taxi. At the same time, Tom and the taxi coninued towards the airport. Tom's mother caught up with the taxi when they were 5 Km from the airport. With his passport in hand, Tom continued to the airport, and his mother turned around and headed home. When Tom arrived at the airport, his mother was still 10 Km from home. Assuming that the taxi and Tom's mother travelled at constant speed over each section of their journey, how far does Tom's mother live from the airport?. Thanks for help.
1) Let D be the distance that Tom has travelled between the time he called his mother and the time she catches up to him.
2) His mother has travelled: D +10
3) By the time he gets to the airport, Tom has travelled: D + 5 since he called his mother, and she has travelled: 10 + 2D.
4) Since the speeds of the 2 vehicles are constant over their respective journeys, the RATIOS of the distances travelled must be the same.
5) In other words: [D+5]/D =[10 + 2D]/[D+10] , solve for D. D = 10 Km. Hence the total distance is:
10 + 10 + 5 = 25 Km. That is my take on it!!!!.
