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
click here to see the step by step solution of the system of equations
the speed of the wind is 20 miles per hour.