Airplanes, flights and wind

Logic Level 3

On a first trip an airplane flies in a straight line from an airport A to an airport B. It then returns in a straight line from B to A. The plane flies at a constant speed and there is no wind.

On a second trip from A to B and back, constant wind blows from A to B. What will the total time of flights (round trip) in this new situation be?

Insufficient information Same time Less than the first trip Higher than the first trip

1 solution

Michael De Seguin
Aug 10, 2017

Let's call plane speed S (in whatever units) and wind speed W in same units. We always have W < S and both are positive. Let's call airport A to airport B distance D (in corresponding units)

Time for round trip with no wind is $\frac {2D}{S}$ , time for round trip with wind (assuming plane speed is exactly to air around it) is $\frac {D}{S + W} + \frac {D}{S -W}$ which we can write $\frac {2DS}{S^2 - W^2}$ after simplifications.

Comparing these two, D simplifies and we are comparing $\frac{2}{S}$ (or $\frac{2S}{S^2}$ ) with $\frac{2S}{S^2 - W^2}$

For denominators, we always have $S^2 - W^2 < S^2$ , so time with wind (inversely proportional to denominators) will always be longer

Airplanes, flights and wind

1 solution

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