Boats and Streams

Upstream and downstream motion

105 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

Boats and Streams problems deal with the motion of a boat in still water and in a flowing stream. These problems involve understanding the effect of the stream's current on the boat's effective speed when moving upstream (against the current) or downstream (with the current).

Key formulas and rules

Speed of boat in still water = (Downstream speed + Upstream speed) / 2

Speed of stream = (Downstream speed - Upstream speed) / 2

Downstream speed = Speed of boat in still water + Speed of stream

Upstream speed = Speed of boat in still water - Speed of stream

Time = Distance / Speed (applies separately for upstream and downstream journeys)

Average speed for round trip = (2 x downstream speed x upstream speed) / (downstream speed + upstream speed)

When a boat travels in still water: Time = Distance / Speed of boat in still water

Key concepts

Downstream Motion

When a boat moves downstream, it travels in the same direction as the stream flow. The stream assists the boat, resulting in a higher effective speed. Downstream speed = Speed of boat in still water + Speed of stream. For example, if a boat's speed in still water is 15 km/h and the stream flows at 3 km/h, the downstream speed is 18 km/h.

Upstream Motion

When a boat moves upstream, it travels against the stream flow. The stream opposes the boat, resulting in a lower effective speed. Upstream speed = Speed of boat in still water - Speed of stream. For example, if a boat's speed in still water is 15 km/h and the stream flows at 3 km/h, the upstream speed is 12 km/h. Note: The boat can only move upstream if its speed in still water exceeds the stream speed.

Still Water and Stream Speed

The speed of a boat in still water is its inherent speed without any current assistance or opposition. The speed of the stream (or current) represents how fast the water is flowing. These two speeds combine to give effective speeds for upstream and downstream travel. When solving problems, always identify what is given (still water speed, stream speed, or effective speeds) and what needs to be found.

Worked examples

Example 1

A boat can travel at 18 km/h in still water. If the speed of the stream is 6 km/h, find: (a) the speed downstream, (b) the speed upstream, (c) the time taken to travel 48 km downstream and return.

Solution

Step 1: Identify given values
Speed of boat in still water = 18 km/h
Speed of stream = 6 km/h

Step 2: Calculate downstream speed
Downstream speed = Speed in still water + Stream speed
Downstream speed = 18 + 6 = 24 km/h

Step 3: Calculate upstream speed
Upstream speed = Speed in still water - Stream speed
Upstream speed = 18 - 6 = 12 km/h

Step 4: Calculate time downstream
Time downstream = Distance / Downstream speed
Time downstream = 48 / 24 = 2 hours

Step 5: Calculate time upstream
Time upstream = Distance / Upstream speed
Time upstream = 48 / 12 = 4 hours

Step 6: Calculate total time
Total time = 2 + 4 = 6 hours

Answer: (a) 24 km/h, (b) 12 km/h, (c) 6 hours

Example 2

A man rows downstream 30 km and upstream 18 km, taking 5 hours each time. Find the speed of the man in still water and the speed of the stream.

Solution

Step 1: Calculate downstream speed
Downstream speed = Distance / Time = 30 / 5 = 6 km/h

Step 2: Calculate upstream speed
Upstream speed = Distance / Time = 18 / 5 = 3.6 km/h

Step 3: Apply formulas for still water and stream speeds
Speed in still water = (Downstream speed + Upstream speed) / 2
Speed in still water = (6 + 3.6) / 2 = 9.6 / 2 = 4.8 km/h

Step 4: Calculate stream speed
Speed of stream = (Downstream speed - Upstream speed) / 2
Speed of stream = (6 - 3.6) / 2 = 2.4 / 2 = 1.2 km/h

Answer: Speed in still water = 4.8 km/h, Speed of stream = 1.2 km/h

Example 3

A boat covers a certain distance downstream in 2 hours, while it takes 4 hours to cover the same distance upstream. If the speed of the stream is 3 km/h, find the speed of the boat in still water.

Solution

Step 1: Define variables
Let speed of boat in still water = x km/h
Speed of stream = 3 km/h

Step 2: Express downstream and upstream speeds
Downstream speed = x + 3 km/h
Upstream speed = x - 3 km/h

Step 3: Since distance is the same for both journeys
Distance downstream = Distance upstream
(Downstream speed) x (Time downstream) = (Upstream speed) x (Time upstream)

Step 4: Set up equation
(x + 3) x 2 = (x - 3) x 4

Step 5: Solve the equation
2x + 6 = 4x - 12
6 + 12 = 4x - 2x
18 = 2x
x = 9 km/h

Answer: The speed of the boat in still water is 9 km/h

Example 4

A man can row 9 km/h in still water. It takes him twice as long to row upstream as to row downstream for the same distance. Find the speed of the stream.

Solution

Step 1: Define variables
Speed in still water = 9 km/h
Let speed of stream = s km/h

Step 2: Express effective speeds
Downstream speed = 9 + s km/h
Upstream speed = 9 - s km/h

Step 3: Use the time relationship
Since time = distance/speed and time upstream = 2 x time downstream for the same distance:
Distance / (9 - s) = 2 x (Distance / (9 + s))

Step 4: Simplify
1 / (9 - s) = 2 / (9 + s)

Step 5: Cross-multiply
9 + s = 2(9 - s)
9 + s = 18 - 2s

Step 6: Solve for s
s + 2s = 18 - 9
3s = 9
s = 3 km/h

Answer: The speed of the stream is 3 km/h

Boats and Streams

Key formulas and rules

Key concepts

Downstream Motion

Upstream Motion

Still Water and Stream Speed

Round Trip Problems

Floating Objects and Relative Motion

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Downstream Motion

Upstream Motion

Still Water and Stream Speed

Round Trip Problems

Floating Objects and Relative Motion

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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