Boats and Streams

Boats and streams problems deal with how the speed of a boat is affected by the current, or stream, it travels through. If a boat's own speed in still water is $x$ km/hr and the stream flows at $y$ km/hr, then travelling downstream (in the same direction as the current) adds the two speeds together, while travelling upstream (against the current) subtracts them.

The relationship also works in reverse. If the boat's downstream speed is known to be $a$ km/hr and its upstream speed is $b$ km/hr, the boat's own speed and the stream's speed can be recovered as their half-sum and half-difference respectively: …