$(4$ points$)$ John and Fred are running along a circular race track whose radius is one mile. Both John and Fred start at the southernmost point on the track. Fred runs clockwise at a rate of $8$ miles per hour. John runs counterclockwise at a rate of $10$ miles per hour. After $\frac{}{72}$ hours have elapsed, at what rate is the distance between John and Fred increasing $($in miles per hour$)?$

Figure $1$: Drawing not to scale