Speed of Stream: Formula, Boats and Streams Methods
Speed of stream is the speed at which water flows in a river or stream. In boat problems, the current increases the boat’s speed downstream and decreases it upstream. This page explains the current speed formula, relations between still-water, downstream and upstream speeds, and methods for solving numerical questions.
What Is Speed of Stream?
Let b be the speed of the boat in still water and s be the speed of the stream. Downstream, the boat moves with the current, so its speed is b + s. Upstream, it moves against the current, so its speed is b − s. Therefore, D = b + s and U = b − s. Adding these equations gives b = (D + U) ÷ 2, while subtracting them gives s = (D − U) ÷ 2. For downstream speed 18 km/h and upstream speed 10 km/h, the stream speed is (18 − 10) ÷ 2 = 4 km/h.
Speed of Stream Formula & Tricks
Important Formulas
The boat’s speed in still water and the stream speed act in the same direction.
The stream opposes the boat’s motion, so its speed is subtracted.
Subtract the upstream speed from the downstream speed and divide by 2.
Add the downstream and upstream speeds and divide by 2.
Use consistent units for distance and time before calculating downstream or upstream speed.
Quick Tricks
When downstream and upstream speeds are given, the stream speed is half their difference. This avoids solving two simultaneous equations.
The boat’s still-water speed is half the sum of its downstream and upstream speeds.
Add the stream speed for downstream motion and subtract it for upstream motion. A speed cannot be negative in an ordinary boat-and-stream question.
Speed of Stream Concepts
Downstream and Upstream Motion
If b is the boat’s speed in still water and s is the stream speed, downstream speed is b + s and upstream speed is b − s. Hence, for b = 15 km/h and s = 4 km/h, the two speeds are 19 km/h and 11 km/h respectively.
Finding Stream Speed from Boat Speeds
Use s = (D − U) ÷ 2. This formula follows from D = b + s and U = b − s. It applies when the given downstream and upstream speeds use the same unit.
Finding Speeds from Distance and Time
If the same distance is covered downstream and upstream, calculate D = distance ÷ downstream time and U = distance ÷ upstream time. The stream speed is then (D − U) ÷ 2. Convert minutes into hours when the distance is in kilometres.
Finding Still-Water Speed
Use b = (D + U) ÷ 2. Equivalently, if the stream speed and one directional speed are known, use b = D − s for downstream data or b = U + s for upstream data.
Round-Trip Time in a Stream
Here d is the one-way distance, b is the still-water speed and s is the stream speed. The average speed for the complete equal-distance journey is 2(b² − s²) ÷ b, not simply the average of the two directional speeds.
Speed of Stream Video Lessons
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Boats: Still-Water and Current Speed
Learn how to find a boat’s speed in still water and the speed of the current using upstream and downstream speed relationships.
Practice Speed of Stream Questions
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Speed of Stream Quick Quiz
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Speed of Stream: Quick Revision
Use these formulas and direction rules for boat-and-stream calculations.
- Downstream speed = boat speed in still water + stream speed.
- Upstream speed = boat speed in still water − stream speed.
- Stream speed = (downstream speed − upstream speed) ÷ 2.
- Still-water boat speed = (downstream speed + upstream speed) ÷ 2.
- Speed = distance ÷ time; convert minutes to hours when distance is measured in kilometres.
- For equal distances, total round-trip time = distance ÷ downstream speed + distance ÷ upstream speed.
- Downstream speed is greater than upstream speed when the stream speed is positive.
Speed of Stream FAQs
What is the current speed formula?
Current or stream speed = (downstream speed − upstream speed) ÷ 2. If the speeds are 20 km/h and 12 km/h, the current speed is (20 − 12) ÷ 2 = 4 km/h.
What is the formula for a boat’s speed in still water?
Still-water speed = (downstream speed + upstream speed) ÷ 2. For speeds of 18 km/h and 10 km/h, it is (18 + 10) ÷ 2 = 14 km/h.
A boat’s downstream speed is 25 km/h and its upstream speed is 15 km/h. What is the stream speed?
Stream speed = (25 − 15) ÷ 2 = 5 km/h.
How are downstream and upstream speeds calculated?
Downstream speed = still-water boat speed + stream speed. Upstream speed = still-water boat speed − stream speed.
A boat covers 30 km downstream in 2 hours and upstream in 3 hours. What is the speed of the stream?
Downstream speed = 30 ÷ 2 = 15 km/h and upstream speed = 30 ÷ 3 = 10 km/h. Stream speed = (15 − 10) ÷ 2 = 2.5 km/h.
Can the upstream speed be zero?
Yes. If the stream speed equals the boat’s still-water speed, upstream speed is b − s = 0, so the boat cannot make forward progress against the current.