In this section, we will discuss about how to solve problems on **Boats and Streams** questions (along with tips and tricks) which are part of **Speed, Time and Distance**.

## Boats and Streams

Let’s get back to our topic boats and streams and discuss different types of questions.

**Case -1** Suppose you are in a motorboat that is running at some speed in the serene ocean so all the speed will be from a boat.

**Case -2** Now your boat is in some river and trying to go opposite to stream, difficult task? in this case speed of the boat is reduced to some extent because the stream is pushing your backside.

**Case -3** Like in case -2 you are in the river but the stream is in same direction to you will face immense speed because the speed of the stream is adding to the boat.

Now let’s get back to the reality, if you were able to imagine all three scenarios then congrats your class is over, all is now a piece of cake. So let’s begin.

**E.g.** man can row with a speed of 6 km/h in still water. How much distance would he cover in 2 hours?

After reading this question you would know that it is case -1

*v* = 6 km/h

*t* = 2 h

Distance = speed × time

⇒ 6 × 2 = 12 km (**Ans**.)

**Upstream Motion**:

If the speed of a boat is against the direction of motion.

**Downstream Motion**:

If the speed of the boat is in the same direction of motion.

Let the speed of a boat in still water be *x * m/s, speed of the stream be *y* m/s, speed of downstream motion be D and speed of upstream motion be U.

1. Speed downstream (D)= (*x + y*) m/s

2. Speed upstream(U) = (*x – y* ) m/s

By these two equations

3. Speed of boat in still water (*x*)= (D + U)/2

4. Speed of stream (*y*) = (D – U )/2

These four are the utmost important formulas of this unit, once fundamentals are clear put the value and find the answer.

**E.g.** A man can row with a speed of 6 km/h in still water. What will be his speed with the

stream, if the speed of the stream is 2 km/h?

*x* = 6 km/h

*y* = 2 km/h

Here the speed of the stream is in same direction of motion, there would be downstream motion.

D = x + y = 6 + 2

⇒ 8 km/h (**Ans**.)

**E.g.** Shantanu can row upstream at 10 km/h and downstream at 18 km/h. Find the man’s rate

in still water and the rate of the current.

⇒ U = 10 km/h, D = 18 km/h (given)

Speed in still water = (D + U)/2

⇒ (10 + 18)/2

⇒ 14 km/h (**Ans**.)

Speed of current = (D – U)/2

⇒ (18 – 10)/2

⇒ 4 km/h (**Ans**.)

As we know x = v / t

For fix distance speed will be inversely proportional to time,

##### Tips and Trick

**⇒**** Time is taken by boat in DS/Time taken in US = Upstream speed/Downstream speed**

**E.g**. A man can row 9 km/h in still water. It takes him twice as long as to row up as to row downstream, find the rate of the stream for the river.

Let he takes *t* time to row downstream so he would take 2*t* time to row upstream and the rate of stream be *x* km/h

According to formula

*t*/2*t* = (9 – *x* )/(9 + *x*)

⇒ 1/2 = (9 – *x*)/(9 + *x*)

⇒ 18 – 2*x * = 9 + *x*

⇒ 3*x* = 9

⇒ *x* = 3 km/h (**Ans**.)

**E.g.** A man can row 12 km/h in still water. When the river is running at 2.4 km/h, it takes him 1 h to row to a place and to come back. How far is the place?

In this situation first, he travels *d* distance in upstream then he returned *d *distance in downstream.

D = 12 + 2.4 = 14.4 km/h

U = 12 – 2.4 = 9.6 km/h

Total time = time in upstream motion + time in downstream motion.

⇒ *d*/9.6 + *d*/14.4 = 1

⇒ *d *[1/9.6 + 1/14.4] = 1

⇒ *d *= 28.8/2 +3

⇒ *d* = 5.76 km (**Ans**.)

__Related Posts__

1. Time and Distance Part 1 – https://www.rankershubindia.com/speed-distance-and-time-part-1/

2. Time and Distance Part 2 – https://www.rankershubindia.com/speed-distance-and-time-part-2/

3. Time and Distance Part 3 – https://www.rankershubindia.com/speed-distance-and-time-part-3/

Click here for Time and Distance Video