Problema Solution
the time for a round trip is 7 3/4 hours. it takes 1850 miles to et there. if the airplane cruises at 480 miles a hour, what is the speed of the wind
Answer provided by our tutors
let
p = 480 mph the plane's speed in still air
w = the speed of the wind, w>0
d = 1,850 mi the distance in one direction
t = 7 3/4 hr = 7.75 hr the time of the round trip
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 => time = distance / speed
traveling against the wind
t1 = d/(p - w)
traveling with the wind
t2 = d/(p + w)
t1 + t2 = t
1850/(480 - w) + 1850/(480 + w) = 7.75
by solving we find:
w = 35.20 mph
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the speed of the wind is 35.20 mph.