A jetliner can fly 7.00 hours on a full load of fuel. Without any wind it flies

Question

A jetliner can fly 7.00 hours on a full load of fuel. Without any wind it flies at a speed of 2.10 102 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 58.0 m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home?

Answer in km

Please explain answer and formula

Explanation / Answer

The time of the jetliner fly t = 7.0h = 25.2*10^3 s The speed of the jet v = 2.10*10^2 m/s the speed of the wind vw = 58m/s from west to east For the round first when the plane towards west the relative speed v1 = 2.10*10^2 - 58 = 152m/s then the time taken for trip due west t1 = x/152 sec when the plane towards east the relative speed v2 = 2.10*10^2 +58 = 268m/s so the time taken for journey t2 = x/268 sec Then the total time t = t1 + t2 25.2*10^3 s = x/152 + x/ 268 therefore the total distance x = 2444*10^3 m or 2444km

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