The **BOAT & STREAM CONCEPTS & PROBLEMS** is very important as there are questions in almost every competitive examination from this topic. The concept **Boat & Stream Concept** is easy to understand and is related to the topic of **Time, Speed and Distance**.here you will get detailed knowledge of BOAT & STREAM CONCEPTS & PROBLEMS

__Introduction to BOAT & STREAM CONCEPTS __

Normally, by speed of the boat or swimmer we mean the speed of the boat (or swimmer) in still water. If the boat moves against the stream then it is called **upstream **and if it moves with the stream, it is called **downstream**.

If the speed of the boat (or swimmer) is X and if the speed of the stream is Y then,

Speed of this boat downstream = (X + Y) km/hr

Speed of this boat upstream = (X -Y) km/hr.

If the speed downstream is X km/hr and the speed upstream is Y km/hr then,

Speed in Still Water = *(X + Y)*2 km/hr

Rate of Stream = *(X – Y)*2 km/hr

Finding average speed if moving with different upstream and downstream speeds

If a man capable of rowing at the speed of X m/sec in still water rows the same distance up and down a stream flowing at a rate of Y m/sec,

Average Speed = *Speed downstream x Speed upstream*Speed in still water

**Average Speed= (X + Y)(X -Y)X**

__Theoram:__

__Theoram:__

**If X km/h be the man’s rate in still water, and Y km/h the rate of current. Then,**

**X+Y= man’s rate with current**

**X-Y=man’s rate against current**

**X= ½ (man’s rate with current + his rate against current).**

**Y= ½ (man’s rate with current – his rate against current).**

Hence, we have the following two facts :

**1).** A man’s rate in still water is half the sum of his rates with and against the current.

**2).** The rate of the current is half the difference between the rates of the man with and against the current.

**Example:** A man can row upstream at 10 km/h and downstream 16 km/h. Find the man’s rate in still water and the rate of the current?

__Solution: __

Rate in still water = *(X + Y)*2

= *(16 + 10)*2 = 13 km/h.

Rate in current = *(X – Y)*2

= *(16 – 10)*2 = 3 km/h.

__Theoram:__

__Theoram:__

**A man can row X km/h in still water. If in a stream which is flowing at Y km/h, it takes him Z hours to row to a place and back the distance between the two places is Z( X^2 – Y^2 )/2X.**

**Example: **A man can row 6 km/h in still water . When the river is running at 1.2 km/h, it takes him 1 hour to row to a place and back. How far is the place?

__Solution: __

Man’s rate downstream = (X + Y)

= (6+1.2)km/h = 7.2 km/h.

Man’s rate upstream =(X – Y)

= (6-1.2)km/h = 4.8 km/h.

Let the required distance be X km. Then

X/7.2 + X/4.8 or 4.8X + 7.2X = 7.2* 4.8

Hence, X = 7.2*4.8/12 = 2.88 km.

**Some problems asked in competitive Exams:**

**1).**A man rows 18 km down a river in 4 hours with the stream and returns in 12 hours. Find his speed and also the speed of the stream?

__Solution: __

Speed with the stream (Downstream)= 18/4 = 4.5 km/h.

Speed against the stream (Upstream) = 18/12 = 1.5 km/h.

Therefore,

Speed of the stream = 1/2(4.5 – 1.5) = 1.5 km/h

And,

speed of the man = 4.5 – 1.5 = 3 km/h.

**2).**The speed of the boat in the still water is 6 km/h, and the speed of the stream is 2 km/h. The boat goes a certain distance down the stream and comes back upstream to the same place from where it started. In the journey, the boat didn’t stop at any point. Find the average speed of the boat in the entire journey?

__Solution:__

Let one side the distance be d km.

Downstream speed = 6+2 = 8 km/h

Similarly, Upstream speed = 6-2 = 4 km/h.

Therefore,

The average speed of the boat = Total distance / Total time = 2d divided by d/8+d/4. Where d = distance.

Then,

2*4*8/4+8 = 16/3 km/h.

**Average Speed= (X + Y)(X -Y)X**= 8*4/6 = 16/3 km/h.

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