Boats & Streams
Boats & Streams
Add current speed for downstream, subtract it for upstream. Recover still-water speed and stream speed by averaging and halving the difference. SSC and banking papers test 2\u20133 questions per exam, typically asking for boat speed, stream speed, or round-trip time.
Key Idea
Downstream = add current; Upstream = subtract current. Still water speed = average of D and U. Stream speed = half their difference. These two formulas solve 80% of boat problems.
Core Formulas
Downstream speed
D = u + v (boat speed + stream speed)
Calculate effective speed when the boat moves with the current \u2014 the stream pushes it faster
Upstream speed
U = u − v (boat speed − stream speed)
Calculate effective speed when the boat moves against the current \u2014 the stream slows it down
Still water speed
u = (D + U) / 2
To find boat's speed in still water from D and U
Stream speed
v = (D − U) / 2
To find stream speed from downstream and upstream speeds
Time for round trip
Total time = d/(u+v) + d/(u−v) = 2du/(u²−v²)
Time for same distance downstream and upstream
Relevant Exams
2–3 questions per exam. Most tested: find boat speed or stream speed given downstream/upstream data. Also tested: time difference for same distance up vs down.