Problema Solution
A certain aircraft can fly 1600 miles with the wind in 5 hours and travel the same distance against the wind in 8 hours. What is 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 = 1600 miles the distance traveled
t1 = 5 hour with the wind
t2 = 8 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)5 = 1600 divide both sides by 5
p + w = 320
traveling against the wind
d = (p - w)t2
(p - w)t2 = d
(p - w)8 = 1600 divide both sides by 8
p - w = 200
by solving the system of equations
p + w = 320
p - w = 200
we find
p = 260 mph
w = 60 mph
click here to see the step by step solution of the system of equations
the speed of the wind is 60 miles per hour.