Problema Solution
Conner flies a plane against a headwind for 5412 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Conner fly the plane when there is no wind?
Answer provided by our tutors
let
d = 5,412 mi the distance traveled in each direction
t = the time of the travel with head wind
t - 16 = the time of the return trip with back wind
w = 8 mph is the wind speed
v = the speed of the plane in still air, v>0
flying with head wind the speed of the plane is: v - w
(v - w)t= d
(v - 8)t = 5412
t = 5412/(v - 8)
flying with back wind the speed of the plane is: v + w
(v + w)(t - 16) = d
(v + 8)(t - 16) = 5412
plug t = 5412/(v - 8) into the last equation:
(v + 8)(5412/(v - 8) - 16) = 5412
by solving we find:
v = 74 mph
click here to see the step by step solution of the equation:
the speed of the plane where there is no wind is 74 mph.