smc

WLOG, let the distance the boat travel be $1$ mile. Then the boat takes $\frac{1}{15+5}=\frac{1}{20}=3$ minutes, to travel down a mile, then to travel back up the river, the boat travels $15-5=10$ miles per hour, taking $\frac{1}{10}=\frac{1}{10}=6$ minutes to travel up the river. This gives an average speed of $\frac{20(3)+10(6)}{3+6}=\frac{120}{9}=\frac{40}{3}$ which as a ratio to $15$ is $\frac{\frac{5\cdot 8}{3}}{3\cdot 5}⟹\frac{8}{9}$ $\boxed{\frac{8}{9}}$