Introduction
Boats & Streams applies the "relative speed" concept from Chapter 15 to water currents — the stream
either helps (downstream) or hinders (upstream) the boat's own speed, and every question in this chapter
reduces to just two formulas.
Core Formulas
| Term | Formula |
|---|
| Downstream Speed | Boat Speed + Stream Speed |
| Upstream Speed | Boat Speed − Stream Speed |
| Boat 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 10 km/h and the stream speed is 3 km/h. Find the downstream and upstream speeds.
Downstream = 10+3 = 13 km/h
Upstream = 10−3 = 7 km/h
Q. A boat covers a distance downstream in 3 hours at 18 km/h, and the same distance upstream in 6 hours. Find the speed of the boat in still water and the speed of the stream.
Distance = 18×3 = 54 km
Upstream speed = 54/6 = 9 km/h
Boat speed = ½(18+9) = 13.5 km/h
Stream speed = ½(18−9) = 4.5 km/h
"Time Ratio" Shortcut
Flowchart — Ratio of Upstream to Downstream Time
For the same distance: Time Upstream : Time Downstream = Downstream Speed : Upstream Speed
This inverse relationship (slower speed → more time) is a fast way to set up ratio-based questions without calculating distance explicitly.
Q. A man rows a boat and takes twice as long to row up as to row down the river. If the speed of the boat in still water is 9 km/h, find the speed of the stream.
Time upstream : time downstream = 2:1 → so downstream speed : upstream speed = 2:1
Let downstream = 2x, upstream = x
Boat speed = ½(2x+x) = 1.5x = 9 → x = 6
Downstream = 12, Upstream = 6
Stream speed = ½(12−6) = 3 km/h
💡 Exam Tip: Whenever a Boats & Streams question gives you two of {boat speed, stream speed, downstream speed, upstream speed}, you can always find the other two using the simple addition/subtraction and averaging formulas above — no complex algebra needed.
✅ Practice Focus: Downstream/upstream speed formulas · Boat speed & stream speed from downstream/upstream values · Time-ratio shortcut for same-distance upstream/downstream trips.