Boat and Stream

When a boat moves in a river or stream, it is affected by the flow of water. The water current either helps (when moving with the flow) or opposes (when moving against the flow) the boat's speed. This leads to two key cases:

Downstream

• The boat moves with the current.

• The stream helps the boat move faster.

• Effective speed = Boat Speed + Stream Speed

Upstream

• The boat moves against the current.

• The stream resists, making it harder to move.

• Effective speed = Boat Speed - Stream Speed

 

Formula

Basic Terminology

Let:

B = Speed of boat in still water (km/hr or m/s)

S = Speed of stream/current (km/hr or m/s)

Then:

Downstream (with the current):

Speed_down= B + S

Upstream (against the current):

Speed_up = B - S

Boat Speed (Still Water): 1/2 ( Downstream Speed + Upstream Speed )

Stream Speed: 1/2 ( Downstream Speed - Upstream Speed )

Time: Distance/Speed

🚤 Question 1

A boat travels 48 km downstream in 3 hours and the same distance upstream in 4 hours.
Find the speed of the boat in still water and the speed of the stream.

✅ Solution:

• Downstream Speed = 48 ÷ 3 = 16 km/h

• Upstream Speed = 48 ÷ 4 = 12 km/h

Now use the formulas:

• Boat's speed in still water = (16 + 12) ÷ 2 = 14 km/h

• Stream's speed = (16 - 12) ÷ 2 = 2 km/h

🟩 Answer:

• Boat speed in still water = 14 km/h

• Stream speed = 2 km/h

🚤 Question 2

A boat covers 60 km downstream in 4 hours and 60 km upstream in 6 hours.
Find the speed of the boat in still water and the speed of the stream.

✅ Solution:

• Downstream Speed = 60 ÷ 4 = 15 km/h

• Upstream Speed = 60 ÷ 6 = 10 km/h

Now use the formulas:

• Boat's speed in still water = (15 + 10) ÷ 2 = 12.5 km/h

• Stream's speed = (15 - 10) ÷ 2 = 2.5 km/h

🟩 Answer:

• Boat speed in still water = 12.5 km/h

• Stream speed = 2.5 km/h