Wind along the route

Problem #3

Tags: simple motion

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Little Orville lays on a river bank and watches tests of a newly built dirigible, being conducted nearby. Large air ship floats majestically along the river - few miles northwards, then back. Wilbur, his elder brother says that the light breeze blowing along the route will hamper speed tests.

"How could it be? - asked Orville, - see, the wind impedes the flight for one half of the route, but then helps for the other!"

Wilbur smiled and proposed a mind experiment: "What if the wind is equal in speed or faster than the aircraft?"

Truly, in this case airship won't be able to return. Actually, that's happened with the first steam-powered dirigible built by Henri Giffard - he demonstrated ability to maneuver along the way - but couldn't fly fast enough back against the wind.

So now Orville is trying to express this in math: airship's engines make it fly with constant speed V through the surrounding air. In still conditions, i.e. without wind, this speed brings the craft there and back in total time T. We want to know what is the total travel time if steady wind is flowing along the route with a speed W (it is guaranteed to be less than V).

Example with numbers:

V = 50
W = 10
T = 4.8

Result should be 5.0.

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