Boats and Streams problems are frequently asked problems in competitive exams.

Stream: Moving water of the river is called stream.

Still Water: If the water is not moving then it is called still water.

Upstream: If a boat or a swimmer moves in the opposite direction of the stream then it is called upstream.

Downstream: If a boat or a swimmer moves in the same direction of the stream then it is called downstream.

Points to remember

  • When speed of boat or a swimmer is given then it normally means speed in still water.

 

Basic Formulas of Boats and Streams

Rule 1: If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

  • Speed of boat or swimmer upstream = (x − y) km/h
  • Speed of boat or swimmer downstream = (x + y) km/h

Rule 2:

  • Speed of boat or swimmer in still water is given by
    Boats and Streams Shortcut Methods
  • Speed of stream is given by
    Boats and Streams Shortcuts

 

Shortcut methods for Boats and Streams

Rule 1: A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man in still water is given by

Boats and Streams Shortcut Formulas

Example

A man goes certain distance against the current of the stream in 2 hour and returns with the stream in 20 minutes.  If the speed of stream is 4 km/h then how long will it take for the man to go 4 km in still water?
Sol:

Let’s say t1 = 20 minutes = 0.33 hours and t2 = 1 hours

Y = 4, then man’s speed in still water

Boats and Streams

So man’s speed is 7.94 km/h in still water.

Now, time taken by the man to row 4 km in still water

Boats and Streams Shortcut Methods

 

Rule 2: A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes him t hours to row to a place and come back, then the distance between two places is given by

Boats and Streams Shortcut Formulas

Example

A man can row 4 km/h in still water. When the water is running at 2 km/h, it takes him 2 hours to go to a place and come back. What is the distance between that place and man’s initial position?
Sol:

Let’s say x = 4 km/h = man’s speed in still water.

y = 2 km/h = water’s speed.

t = 2, so

Boats and Streams Shortcuts

 

Rule 3: A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is given by

Boats and Streams Shortcut Formulas

Example

A man can row 4 km/h in still water. The water is running at 2 km/h. He travels to a certain distance and comes back. It takes him 2 hours more while travelling against the stream than travelling with the stream. What is the distance?
Sol:

Let’s say x = 4 km/h = man’s speed in still water.

y = 2 km/h = water’s speed.

t = 2, so

Boats and Streams Shortuct Formulas

 

Rule 4: A man can row in still water at x km/h. In a stream flowing at y km/h, if he rows the same distance up and down the stream, then his average speed is given by

Boats and Streams

Boats and Streams Shortcut Methods

Example

Speed of boat in still water is 9 km/h and speed of stream is 2 km/h. The boat rows to a place which is 47 km away and comes back in the same path. Find the average speed of boat during whole journey.
Sol:

Let’s say x = 9 km/h = speed in still water

Y = 2 km/h = speed of stream

Boats and Streams Shortcuts