Problema Solution
A plane travels at a speed of
210 mph in still air. Flying with a tailwind, the plane is clocked over a distance of
675 miles. Flying against a headwind, it takes
1 hour longer to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)
Answer provided by our tutors
Let
v = 210 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 = 210 + w is the speed of the plane when flying with tailwind
v - w = the speed of the plane when flying with headwind
since speed = distance/time follows time = distance/speed
d/(v - w) + 1 = d/(v + w)
675/(210 - w) + 1 = 675/(210 + w)
........
........
w = 1381.9 mph
The wind velocity was 1381.9 mph.