Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far behind is Foley, in km?
If $A$ is 10 km behind and $B$ is 15 km behind, that means that the ratio of their speeds is $\dfrac BA=\dfrac 34$. Therefore, for every $3$ km that Edith runs, Foley runs $4$. When Edith finishes the race, the total distance run is $24$ km, or $8 \times 3$ km. During this time, Foley will have run $8 \times 4 = 32$ km. Therefore, Foley will be $32 - 24 = \boxed{8\text{ km}}$ behind.
