A Race Around the Globe

Assume that all of the competitors fly the same entire great circle (in the same direction) with the same starting and finishing point, (and that they all start at the same time).

Let the respective (constant) speeds of Alice, Bob, Carly and Dave be $\large v_{a}, v_{b}, v_{c}$ and $\large v_{d}.$

Now rather than looking at distances traveled, it may be easier to look at the central angles of the arcs traveled by each of the competitors after a certain time. Since $\large v_{a} = 2v_{b},$ Bob will have "traveled" $\pi$ radians around the great circle at the time Alice finishes. Then since $\large v_{b} = 3v_{c}$ Carly will have only traveled $\dfrac{\pi}{3}$ radians by the time Alice finishes, and so the distance $D$ is represented by an arc along the great circle with a central angle of $\dfrac{\pi}{3}$ radians.

Next, since when Bob finishes he and Dave are a distance $D$ apart, Dave is in the same position relative to Bob as Carly was to Alice at the time Alice finished. This implies that

$\large \dfrac{v_{c}}{v_{a}} = \dfrac{v_{d}}{v_{b}} \Longrightarrow v_{c} = \dfrac{v_{a}}{v_{b}} * v_{d} = 2v_{d},$

and so $\large v_{a} = 2v_{b} = 2*3v_{c} = 2*3*2v_{d} \Longrightarrow \dfrac{v_{a}}{v_{d}} = 2*3*2 = \boxed{12}.$