Problema Solution
If you are flying to a city 800 miles away, what will be the difference in flight time between flying into a 40-mph headwind and flying with a 40-mph tailwind if the plane's maximum speed with no wind is 160-mph?
Answer provided by our tutors
let
p = 160 mph the plane's speed in still air
w = 40 mph the speed of the wind
d = 800 miles the distance traveled
t1 = hours traveled with the wind
t2 = hours traveled against the wind
t2 - t1 = ? the difference in flight time
the speed of the plane traveling against the wind is:
p - w = 160 - 40 = 120 mph
the speed of the plane traveling with the wind is:
p + w = 160 + 40 = 200 mph
since speed = distance/time => time = distance/speed
traveling with the wind (with tailwind)
t1 = d/(p + w)
t1 = 800/200
t1 = 4 hr
traveling against the wind (with headwind)
t2 = d/(p - w)
t2 = 800/120
t2 = 20/3 hr
t2 = 6 hr 2*60/3 min
t2 = 6hr 40 min
the difference in time flight is
t2 - t1 = 6 hr 40 min - 4 hr = 2 hr 40 min
the difference in flight time is 2 hr 40 min.