Question

When a plane flies with the​ wind, it can travel 1575 miles in 3.5 hours. when the plane flies in the opposite​ direction, against the​ wind, it takes 4.5 hours to fly the same distance. find the average velocity of the plane in still air and the average velocity of the wind?

Answer 1

When plane is flying along the wind then we can say

`V_(plane) + v_(wind) = (distance)/(time)`

`V_(plane) + v_(wind) = (1575)/(3.5)`

`V_(plane) + v_(wind) = 450 mph`

Now when its going against the wind the speed is given by

`V_(plane) - v_(wind) = (distance)/(time)`

`V_(plane) - v_(wind) = (1575)/(4.5)`

`V_(plane) - v_(wind) = 350 mph`

Now by the above two equations we will have

`V_(plane) = 400 mph`

`v_(wind) = 50 mph`