Problema Solution
A passenger airliner is flying a round trip from New York City to San
Francisco (2,500 miles 1-way). The round-trip flight time is 10 hours
and 25 mins. (Does not count the layover time). Given that the speed
of the wind during the round-trip is constant, calculate the speed of
the wind if the speed of the aircraft is 500 mph.
Answer provided by our tutors
Let
w = the speed of the wind, w>0
v = 500 mph the speed of the aircraft in still air
d = 2,500 the distance in one direction
t = 10 hr 25 min = 10 + 25/60 = 125/12 hr the total time of the travel
Since speed = distance/time follows time = distance/speed
Traveling with a tale wind the speed of the plane is: v + w = 500 + w
Traveling with head wind the speed of the plane is: v - w = 500 - w
d/(v + w) + d/(v - w) = 125/12
2500/(500 + w) + 2500/(500 - w) = 125/12
........
........
w = 100 mph
The speed of the wind is 100 mph.