Problema Solution
A plane travels at a speed of
150
mph in still air. Flying with a tailwind, the plane is clocked over a distance of
675
miles. Flying against a headwind, it takes
2
hours longer to complete the return trip. What was the wind velocity?
Answer provided by our tutors
Let
v = 150 mph the speed of the plane in still air
w = the wind velocity, w>0
d = 675 mi the distance that the plane flew in each direction
v + w = 150 + w is the speed of the plane when flying with tailwind
v - w = 150 - w the speed of the plane when flying with headwind
since speed = distance/time follows time = distance/speed
d/(v - w) + 2 = d/(v + w)
675/(150 - w) + 2 = 675/(150 + w)
........
........
w = 706.83 mph
The wind velocity was 706.83 mph.