Ava’s father George picks her up at the train station when she comes home from school, then George drives Ava home. They always return home at 5:00 pm. One day Ava left school early and got to the train station an hour early. She then started walking home. George left home at the usual time to pick Ava up, and they met along the route between the train station and their house. George picked Ava up and then drove home, arriving at 4:48 pm. For how many minutes had Ava been walking before George picked her up?

Answer 1

To solve the problem, we need to analyze the situation with the information provided.

1. Usual Schedule: Ava and her father George arrive home at 5:00 pm. This means that if George drives directly from the train station to their home, the total travel time for both on a normal day would be the same, leading to their consistent 5:00 pm home arrival.

2. Ava's Early Arrival: Ava left school early, arriving at the train station 1 hour before the usual time. Since they normally arrive at 5:00 pm, it implies:

   • If George picks her up at a time that usually allows them to arrive home by 5:00 pm, and she aligns this with her timeline, we can conclude that she usually arrives at the train station at 4:00 pm (the hour before they go home).

3. Walking Home: Ava arrives at 3:00 pm, which means she starts walking home at 3:00 pm.

4. George’s Departure and Time of Pickup:

   • George leaves home at the usual time (let's denote it as \( t \)).
   • Since Ava and George always meet and go home together, we need to now find how long Ava walked before she was picked up (which we'll denote as \( x \) minutes).
   • George picks Ava up, and they arrive home at 4:48 pm.

5. Total Drive Time: From the time they leave the meeting point until they get home is:

   • 5:00 pm (usual time) - 4:00 pm (time they normally start the trip) = 12 minutes earlier than usual.
   • Since they arrived home at 4:48 pm, George spent 12 minutes on the drive back (meaning George has a net 15-minute drive which also accommodates 3 minutes earlier thus managing to arrive at home).

6. Conclusion: Therefore, we need to establish that:

   • Normally , it takes 15 minutes from the train station to home which means \( \text{Time for George to meet Ava = 4:48 - 3 minutes (to home)} = 4:45</sup> \) at least he meets her before they head home. Ava would have spent \( 15 - 3 = 12\) minutes of normal total travel time before the pickup satisfactorily qualifying to 48-45. Thus while she walked she spent:

• \( \text{Walking time:} = 4:45 - 3:00 = 12 \) or \( \text{3:00 to 4:45}\) being precisely 45 minutes

Therefore, Ava had been walking for 45 minutes before George picked her up!