Problema Solution
A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 12 minutes. What is the plane's speed in still air, and how fast is the wind blowing?
Answer provided by our tutors
let
p = the plane's speed in still air
w = the speed of the wind
d = 180 miles
t1 = 2 hours the time traveling against the wind
t2 = 1 hours 12 min = 1 12/60 hours = 1.2 hours the time traveling with 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
d = (p - w)t1
180 = (p - w)2
(p - w)2 = 180 divide both sides by 2
p - w = 90
d = (p + w)t2
(p + w)1.2 = 180 divide both sides by 1.2
p + w = 150
by solving the system of equations
p - w = 90
p + w = 150
we find
p = 120 mph
w = 30 mph
click here to see the step by step solution of the equations
the speed of the plan in still air is 120 mph.
the wind is blowing with 30 mph.