Respuesta :
Let [tex] v_h [/tex] be the speed of the helicopter in still air. Let [tex] v_w [/tex] be the speed of the wind. Then, from the given information,
[tex] (v_h-v_w)2=168\\
(v_h+v_w)2=252\\ [/tex]
Adding the above 2 equations,
[tex] 4v_h=168+252\\
4v_h=420\\
v_h=105 [/tex]
The speed of the helicopter in still air [tex] 105 \;mi/hour [/tex]
V = speed of helicopter
v = speed of wind
V - v = speed of helicopter against the wind
d = distance traveled against the wind = 168 mi
t = time of travel = 2 h
using the equation
speed = distance/time
V - v = d/t
V - v = 168/2
V - v = 84
v = V - 84 eq-1
V + v = speed of helicopter with the wind
D = distance traveled with the wind = 252 mi
t = time of travel = 2 h
using the equation
speed = distance/time
V + v = D/t
V + v = 252/2
V + v = 126
using eq-1
V + V - 84 = 126
V = 105 mph
