Answer
$10.8$ miles.
Work Step by Step
Let it enter the layer at $(x_1,-4)$ and leave at $(x_2,-4)$.
Then $x_1^2+(-4)^2=15^2\\x_1^2=209\\x_1\approx\pm14.6$
As we can see $x_1$ is negative, thus $x_1=-14.6$.
$x_2^2+(-4)^2=10^2\\x_1^2=84\\x_1\approx\pm9.2$
As we can see $x_1$ is negative, thus $x_2=-9.2$.
Then the distance is: $|x_1-x_2|=|-14.6-(-9.2)|=5.4$
Since the figure is symmetric, it will cover the same amount of space in the fourth quadrant as well, thus the answer is: $2\cdot5.4=10.8$
