#### Boats and Streams Shortcut Methods

Boats and Stream questions 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

=1/2(Downstream + Upstream)

- Speed of stream is given by

=1/2(Downstream - Upstream)

#### 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 =y{(t2+t1)/(t2-t1)}km/h

**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 t24= 1 hours

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

=y{(t2+t1)/(t2-t1)

=4{(1+0.33)/(1-0.33)}=(4*1.33/0.63)=7.94km/h

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

=4*1/7.94=0.504 hours=30.23 min.

**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

=t{(x^2-y^2)/2x}

**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

Distance =2{4^2-2^2)/4*2}=2*12/8=3 km

**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=t{(x^2-y^2)/2y}

**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

Distance =2{4^2-2^2)/2*2}=2*12/4=6 km

**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

**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

Average speed=(x^2-y^2)/x=(9^2-2^2)/9=8.55 km/h

#### Boat & streams concept

**Concept | Practice set 1 | Practice set 2**

**Download Concept as a pdf form click below link**