Introduction
Boats & Streams applies relative speed to a boat moving in water with a current. When the boat moves with the
current (downstream), the speeds add; against the current (upstream), they subtract.
Core Formulas
| Term | Formula |
|---|
| Downstream speed | Boat speed (b) + Stream speed (s) |
| Upstream speed | Boat speed (b) − Stream speed (s) |
| Boat's speed in still water | ½ × (Downstream speed + Upstream speed) |
| Stream speed | ½ × (Downstream speed − Upstream speed) |
Q. A boat's speed in still water is 15 km/hr and the stream speed is 3 km/hr. Find the time taken to travel 36 km downstream.
Downstream speed = 15+3 = 18 km/hr. Time = Distance/Speed = 36/18 = 2 hours.
Q. A man rows downstream at 20 km/hr and upstream at 8 km/hr. Find his speed in still water and the speed of the stream.
Boat speed = ½(20+8) = 14 km/hr. Stream speed = ½(20−8) = 6 km/hr.
⚠️ Key Insight: If a question gives downstream and upstream speeds directly, you can find both
the boat's still-water speed and the stream speed instantly using the sum/difference formulas — no need to set
up separate equations.
💡 Exam Tip: Boats & Streams questions are essentially Time-Speed-Distance in disguise —
apply the same time = distance/speed logic once you've computed the effective (downstream/upstream) speed.
✅ Practice Focus: Downstream/upstream speed and time calculation · Finding boat and stream speed
from given downstream/upstream values · Round-trip average speed problems.