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
.