🧭 Finding Boat & Stream Speed

If a leg gives a distance and a time, first turn it into a speed with $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ (convert minutes to a fraction of an hour before dividing). That gives you downstream $D = b+s$ and upstream $U = b-s$.

Then add and halve for the boat, subtract and halve for the stream:

$b = \dfrac{D+U}{2}$  ·  $s = \dfrac{D-U}{2}$.

• Two-journey problems: when each trip mixes some upstream and some downstream distance for a total time, write one equation per trip in $U$ and $D$: $\dfrac{\text{up}}{U} + \dfrac{\text{down}}{D} = \text{time}$. Don't grind the algebra — test the HCF of the downstream distances for $D$ and check it fits both rows.

• Equal-time clue: if up and down take the same time, distance is proportional to speed, so the distance ratio is the speed ratio $U:D$.