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

$V_{plane} + v_{wind} = \frac{distance}{time}$

$V_{plane} + v_{wind} = \frac{1575}{3.5}$

$V_{plane} + v_{wind} = 450 mph$

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

$V_{plane} - v_{wind} = \frac{distance}{time}$

$V_{plane} - v_{wind} = \frac{1575}{4.5}$

$V_{plane} - v_{wind} = 350 mph$

Now by the above two equations we will have

$V_{plane} = 400 mph$

$v_{wind} = 50 mph$