## Boat and Stream Problems are one of the important bits for all competitive exams.

Boat and Stream problems are frequently asked problems in Competitive Exams and Entrance Exams. Here we explain some key points about Boat and stream problems and Tips & tricks to solve any problem less than 45 seconds.

In Boat and Stream we must aware about what is Upstream and Downstream.

**Stream: **Moving water of the river is called stream.

**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.

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

**Note : **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 kmph and the speed of stream is y kmph then,

- Speed of boat or swimmer upstream = (x − y) kmph
- Speed of boat or swimmer downstream = (x + y) kmph

**Rule 2:**

- Speed of boat or swimmer in still water is given by

- Speed of stream is given by

**Shortcut methods for Boats and Streams**

**Type 1:**

A man can row certain distance downstream in t_{1} hours and returns the same distance upstream in t_{2} hours. If the speed of stream is y km/h, then the speed of man in still water is given by

**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 t_{1} = 20 minutes = 0.33 hours and t_{2} = 1 hours

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

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

**Type 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

**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

Tricks and Tips on Boat and Stream problems

**Type 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

**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

**Type 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

**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

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