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Progetto Olimpiadi di Matematica GARA di SECONDO LIVELLO, 2005

Algebra Difficulty 4.3 AIME Find the answer Italy

Problem:

Edoardo went on vacation to the city of Altanbulat. His flight, on the way there, departed from Milan at 13:00 and arrived in Altanbulat at 9:00 the following day (local time). The return flight instead departed from Altanbulat at 9:00 and landed at 15:00 the same day in Milan (again, all the times indicated are according to local time zone). Assuming that the two trips had the same actual duration, what is the time zone difference between Italy and Altanbulat?

Pick one

Solution

Solution:

The answer is (C). Let us denote by $d$ the time zone difference between Italy and Altanbulat. Translating all the times into the Italian time zone, Edoardo departs at 13 and arrives at $9-d$ the following day, so he takes $24+(9-d)-13=20-d$ hours for the outbound trip. On the return, instead, he departs at $9-d$ and arrives at 15, so he takes $15-(9-d)=6+d$ hours. Equating the durations of the two trips we obtain $20-d=6+d$ , whose only solution is $d=7$ . Therefore the time zone difference is 7 hours and the trip has an actual duration of 13 hours.

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.