Answer
Explanation given below.
Work Step by Step
Testing the velocities at t=4 and t=15 hours,
$\left[\begin{array}{ll}
t=4 & t=15\\
v(4)=475-50(4) & v(15)=475-50(15)\\
v(4)=275 & v(15)=475-750\\
& v(15)=-275
\end{array}\right]$
The velocity at $t=15$ is negative, which would mean that the flight direction is backwards (in the direction opposite to the one the plane is pointing to).
This could 'happen' if the plane doesn't touch down after 4 hours, but continues to fly in the same direction, overshooting the destination.
Due to the headwind, the velocity would decrease until it reaches 0 mph, after which it would increase in the opposite direction (backward) towards the destination. The 'touchdown' would be performed in reverse. This is nonsense, which is why we discard 15 hours as the duration of the flight.
