Respuesta :
The speed of an object is given by:
[tex]v=\frac{d}{t}[/tex]For the first part we know that the helicopter can travel 425 miles against a 935 headwind, the resultant speed of the helicopter will be its speed in still air minus the velocity of the wind, then we have:
[tex]\begin{gathered} v_h-935=\frac{425}{t} \\ t=\frac{425}{v_h-935} \end{gathered}[/tex]For the scond part the resultant speed of the helicopter is the velocity of the wind plus the velocity of the helicopter, then we have:
[tex]\begin{gathered} v_h+935=\frac{775}{t} \\ t=\frac{775}{v_h+935} \end{gathered}[/tex]Since the time is equal we have that:
[tex]\begin{gathered} \frac{425}{v_h-935}=\frac{775}{v_h+935} \\ 425(v_h+935)=775(v_h-935) \\ 425v_h+397375=775v_h-724625 \\ 775v_h-425v_h=724625+397375 \\ 350v_h=1122000 \\ v_h=\frac{1122000}{350} \\ v_h=3205.71 \end{gathered}[/tex]Therefore, the velocity of the helicopter is 3205.72 mph
