Problema Solution

An airplane can fly with the wind a distance of 800 miles in 4 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

Answer provided by our tutors

let


p = the plane's speed in still air

w = the speed of the wind

d = 800 miles the distance traveled

t1 = 4 hour with the wind

t2 = 5 hours against the wind


the speed of the plane traveling against the wind is: p - w

the speed of the plane traveling with the wind is: p + w


since speed = distance/time => distance = speed*time


traveling with the wind


d = (p + w)t1


(p + w)4 = 800 divide both sides by 4


p + w = 200


traveling against the wind


d = (p - w)t2


(p - w)t2 = d


(p - w)5 = 800 divide both sides by 5


p - w = 160


by solving the system of equations


p + w = 200

p - w = 160


we find


p = 180 mph


w = 20 mph


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the speed of the wind is 20 miles per hour.