Air travel between cities of different time zones
Cities A and B are in different time zones. A is located 3000 km east of B. The schedule of an airline operating non-stop flights between A and B is as follows. (All the times indicated are local and on the same day). Departure from B 8 AM ; Arrival at A 3 pm; Departure from A 4 PM; Arrival at B 8 pm. Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind flowing from east to west at 50 km per hour.
What is the time difference between A and B (in hours)?
The answer is 1.
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1 solution
The plane leaves city B at 8:00 am and arrives back at city B at 8:00 pm. Thus it is away for 12 hours, 1 hour of which it is not travelling (between 3:00 pm and 4:00 pm at city A). Thus, in a total of 11 hours, the plane travels 3000 km at speed (x – 50) and 3000 km at speed of (x + 50). So,
3 0 0 0 / ( x − 5 0 ) + 3 0 0 0 / ( x + 5 0 ) = 1 1
Plugging the given options of the speeds, we see that x = 550 satisfies the equation. Now, time taken from B to A is 3000/(550 – 50) = 6 hours, and hence the plane reaches A at 8:00 am + 6 hrs i.e. 2 pm. But the time then at A is 3 pm. Thus the time difference between the two cities is 1 hour.