# How To Solve Boats And Streams Problems Quickly

## How to Solve Quickly Boats and Streams

In water, the direction along the stream is called downstream and, the direction against the stream is called upstream.
The boats and streams problems are based on the concepts of time, speed, and distance. However, a few adjustments need to be made in case of such problems. There are two variations of these problems. ## Type 1: How to Solve Speed of Boat Problems

### Question 1:

A boat covers 900 meters in 300 seconds against the stream and returns downstream in 3 minutes. What is the speed of the boat in still water?

Options:

1. 4 m/s
2. 5 m/s
3. 1 m/s
4. 3 m/s

#### Solution:

upstream speed = 900/300 = 3m/s

Downstream speed = 900/3 * 60 = 900/180 = 5m/s

Speed in still water = 1/2 (speed downstream + speed upstream)

= 1/2 (5 + 3)

= ½ (8)

= 4 m/s

### Question 2:

The speed of a ship in still water in 20 km/hr and the rate of current is 15 km/hr. The distance travelled downstream in 4 minutes is:

Options:

1. 2.333 km/hr
2. 3.5 km/hr
3. 1.2 km/hr
4. 4 km/hr

#### Solution:

Speed downstream = (20 + 15) km/h = 35 km/h

Distance covered in 4 minutes = 35 * 4/60 = 2.333 km/hr

### Question 3:

Find the ratio of the speed of the boat and the stream if Rakesh takes twice as long to row a distance in favour of the stream as to row the same distance against the stream.

Options:

1. 1:2
2. 3:1
3. 4:5
4. 1:1

#### Solution:

Let the Rakesh’ upstream speed = x

Downstream speed = 2x

(Speed in still water): (Speed of stream) = 2x + x/ 2: 2x – x/2 = 3: 1

## Type 2: How to Solve, Find the Speed of Stream

### Question 1:

What is the speed of the stream, if the speed of the boat against the stream is 6 km/hr and the speed of a boat in still water is 10km/hr?

Options:

1. 4 km/hr
2. 2 km/hr
3. 10 km/hr
4. 5 km/hr

#### Solution:

Let the speed of stream = x

Speed of boat = 10 km/hr

Upstream speed = 6 km/hr

We know that, Upstream speed = speed of boat – speed of stream

6 = 10 – x

x = 10 – 6

x = 4 km/hr

### Question 2:

A man can row a boat upto 30 km down a river in 3 hours with the stream and can return back in 5 hours. What is the speed of the stream?

Options:

1. 4 km/hr
2. 2 km/hr
3. 6 km/hr
4. 5 km/hr

#### Solution:

Speed Downstream= 30/3 = 10 km/hr

Speed Upstream = 30/5 = 6 km/hr

Speed of the stream = 1/2(10 – 6) = 2 km/hr

### Question 3:

A man sail a boat to a place which is 24 km far. He reaches that place and comes back in 7 hours. He finds that he can sail a boat 3 km downstream in the same time as 2 km upstream. Find out the rate of the stream?

Options:

1. 1.25 km/hr
2. 2 km/hr
3. 6 km/hr
4. 5 km/hr

#### Solution:

Suppose, He moves 3km downstream in x hours = 3/x km/hr

Speed Upstream = 2/x km/hr

24/(3/x) + 24/(2/x) = 7

= 6/15

= 0.4

So, Downstream Speed = 3/x = 3/ 0.4 = 7.5 km/hr

Upstream Speed = 2/0.4 = 5 km/hr

Rate of the stream = 1/2 (7.5 – 5) = 2.5/2 = 1.25 km/hr

## Type 3: Using Man’s Still Water Speed Calculate Stream’s Speed

### Question 1:

Rahul can sail a boat 3 quarters of kilometer upstream in 11 minutes and downstream in 7 minutes. Find out the speed of Rahul in still water?

Options:

1. 9 km/ hr
2. 5 km/ hr
3. 4 km/ hr
4. 3 km/ hr

#### Solution:

Three-quarters of a kilometer = 750 meter

11(1/4) minutes = 45/4 = 675 seconds

7(1/2) minutes = 15/2 = 450 seconds

Upstream speed = 750/675 = 10/9 m/sec

Downstream speed = 750/450 = 5/3 m/sec

Speed in still water = ½ (10/9 + 5/3) = 25/18m/sec

To convert it into km/hr, multiply 25/18 by 18/5

= 5 km/hr

### Question 2:

A man’s speed with the current is 20 km/hr and the speed of the current is 5 km/hr. What is the man’s speed against the current?

Options:

1. 20 km/hr
2. 15 km/ hr
3. 5 km/ hr
4. 10 km/ hr

#### Solution:

Man’s speed with the current = 20 km/hr
speed of the man + speed of the current = 20 km/hr
speed of the current is 5 km/hr
Hence, speed of the man = 20 – 5 = 15 km/hr
Man’s speed against the current = speed of the man – speed of the current
Man’s speed against the current = 15 – 5 = 10 km/hr

### Question 3:

If a man sails a boat at the rate of 5 km/hr in still water. His upstream rate is 3 km/hr, then find the man’s speed along the current?

Options:

1. 7 km/hr
2. 5 km/hr
3. 8 km/hr
4. 10 km/hr

#### Solution:

Let the speed along with the current = x km/hr

Therefore, (x+3)/2 = 5

x = 7km/hr