smc

Suppose the first half of the trip's distance is called $x$. Then the time for the first half is $\frac{x}{50},$ and the second half's time is $\frac{x}{45}$, so the total time is $\frac{x}{50}+\frac{x}{45}$, so the speed is $\frac{2x}{\frac{x}{50}+\frac{x}{45}}=\frac{2x}{\frac{19x}{450}}=2x\cdot \frac{450}{19x}=\frac{900}{19}=47\frac{7}{19}$, so the answer is $\boxed{47\frac{7}{19}}$.