Say, the time zone of New Delhi is 5 hours and 30 minutes ahead of London.
I have the following data. A flight departing at 10:00am from New Delhi lands at 02:30pm in London. A flight departing at 05:00am from London lands at 08:30pm in New Delhi.
All times are in local time.
I’m required to calculate the flight duration in hours between New Delhi and London.
The answer goes as follows:
For New Delhi to London, the difference between 10:00am and 02:30pm is 4.5 hours. Similarly, for London to New Delhi, the difference is 15.5 hours.
Taking the average of these two — 4.5 and 15.5 hours gives me 10 hours, which is the required answer.
The problem is, I do not understand this last step, as to why we are taking the average. In my head, my brain is stuck to the idea that we have to take the difference of 15.5 and 4.5, and the answer should be 11 hours (which is wrong). I’m sure the explanation is simple but I cannot figure it out.
The "calculated" flight time going one way is the "real" flight time plus the time zone difference. In the opposite way it is the "real" flight time minus the time zone difference: $$t_{N-L}=t_R-\Delta t\\t_{L-N}=t_R+\Delta t$$ Adding these two equations together you get $$t_{N-L}+t_{L-N}=2t_R$$ So: $$t_R=\frac{t_{N-L}+t_{L-N}}2$$ Notice that's independent of the time zone difference.