1957 AHSME Problems/Problem 20

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