This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Is a round-trip by airplane longer or shorter if there is wind blowing?
It will take longer, by the ratio (s^2)/(s^2 - w^2) where s is the
plane's speed, and w is the wind speed. The stronger the wind the
longer it will take, up until the wind speed equals the plane's speed,
at which point the plane will run out of fuel before too long.
s = plane's speed w = wind speed d = distance in one direction d / (s + w) = time to complete leg flying with the wind d / (s - w) = time to complete leg flying against the wind d / (s + w) + d / (s - w) = round trip time d / (s + w) + d / (s - w) = ratio of flying with wind to ------------------------- flying with no wind (bottom of d / s + d / s equation is top with w = 0) this simplifies to s^2 / (s^2 - w^2).