Question

Mary takes a sightseeing tour on ahelicopter that can fly 425 miles against935 mph headwind. In the same amountof time it can travel 775 miles with 935 mph tailwind. Find the speed of the helicopter

Answer 1

The speed of an object is given by:

`v=(d)/(t)`

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:

`\begin{gathered} v_h-935=(425)/(t) \\ t=(425)/(v_h-935) \end{gathered}`

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:

`\begin{gathered} v_h+935=(775)/(t) \\ t=(775)/(v_h+935) \end{gathered}`

Since the time is equal we have that:

`\begin{gathered} (425)/(v_h-935)=(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=(1122000)/(350) \\ v_h=3205.71 \end{gathered}`

Therefore, the velocity of the helicopter is 3205.72 mph