🔁 Round Trip & Return Journey

Net speeds first: $D = b+s$ and $U = b-s$. The total there-and-back time is $\dfrac{d}{D} + \dfrac{d}{U}$.

• When the round-trip time $T$ is given and you need the one-way distance, skip adding fractions and use $d = \dfrac{T \times D \times U}{D+U}$ (cancel $T$ against $D+U$ before multiplying).

• The round-trip average speed is $\dfrac{D \times U}{b}$, not the plain average of $D$ and $U$ — the slow upstream leg drags the average below the midpoint.

• Speed-doubling puzzles fall out of the round-trip time formula $T = \dfrac{2bd}{b^2 - s^2}$: take the ratio of the two cases and the distance cancels.