# Boat and Stream Problem Concept

## Boat and Stream Problem Tips and Tricks

**Still water: **The water of a river or any other water body which is not flowing is known as still water.

**Stream: **It is the flowing water of a river which is moving at a certain speed.

**Downstream: **In water direction along the stream is called downstream.

**Upstream: **In water direction against stream is called upstream.

**Rule: **If the speed of a boat in still water is x km/hr and the speed of the stream is y km/hr, then:

## Formula

Speed downstream = ( x + y ) km/hr Speed upstream = ( x - y ) km/hr

**Rule: **If the downstream speed is a km/hr and the speed upstream is b km/hr, then

## Formula

Speed in Still water = 1/2(a+b) Rate of Stream = 1/2(a-b)

**Question 1: **A boatman rows his boat 48 km upstream and same distance downstream. The boat takes 12 hrs and 8 hrs to go upstream and downstream respectively. Find the speed of the boat in stagnant water and the speed of the stream respectively.

- (A). 4 km/hr ; 3 km/hr
- (B). 5 km/hr ; 1 km/hr
- (C). 6 km/hr ; 4 km/hr
- (D). 12 km/hr ; 6 km/hr
- (E). Cannot be determined

**Answer: **(B). 5 km/hr ; 1 km/hr

## Explanation

Man's/Boat's Speed = X Stream/Current/River Speed = Y ∴ Downstream speed = X + Y Upstream speed = X - Y Downstream Speed = Distance covered/Time taken = 48/8 = 6 km/hr Upstream Speed = Distance covered/Time taken = 48/12 = 4 km/hr X+Y = 6 km/hr and X-Y = 4 km/hr Adding them we get, X+Y+X-Y = 10 km/hr ∴ X=5 km/hr = Speed of Boat Y=6-5 = 1 km/hr = Speed of stream

**Question 2: **The time taken by swimmer to swim upstream is 4 hours more than the time he takes to swim downstream. He swims at a speed of 10 km/hr in still water. The stream is flowing gently at 2 km/hr. What is the swimming distance one side?

- (A). 20 km
- (B). 72 km
- (C). 80 km
- (D). 96 km

**Answer: **(D). 96 km

## Explanation

Man's/Boat's Speed = X Stream/Current/River Speed = Y ∴ Downstream speed = X + Y Upstream speed = X - Y X+Y = 10+2 = 12 km/hr and X-Y = 10-2 = 8 km/hr Let Time be T hours for downstream Distance is same ∴ D = D ∴ 12 x T = 8 x (T+4) ∴ T = 8 hours = Time for downstream Distance = 12km/hr x 8 hours = 96 km

**Question 3: **A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

- (A). 4
- (B). 5
- (C). 6
- (D). 10

**Answer: **(B). 5

## Explanation

Let the speed of the stream be x km/hr. Then, Speed downstream = (15 + x) km/hr, Speed upstream = (15 - x) km/hr. 30/(15+x) + 30/(15-x) = 9/2 =900/225-x^{2}= 9/2 9 x^{2}= 225 x^{2}= 25 x = 5 km/hr

**Question 4: ** A man can row 15 km /hr in still water. It takes him twice as long to row upstream as to row downstream. Find the rate of stream ?

## Solution

Let man's rate in upstream be x km/hr, then his rate in downstream is = 2x kmph rate is still water = 1/2(2x+x) 3x/2 km/hr 3x/2 = 15, x = 10km/hr So rate in down stream= 2x= 20 km/hr Rate of stream = 1/2(20-10) = 5km/hr

**Question 5: ** A man can swim 6 km / hr in still water. If river's rate is 2 km / hr, it takes the man 3 hours to row to a place and back. How far is the place ?

## Solution

Man's rate in upstream=( 6 - 2 ) km/hr = 4 km/hr Man's stream rate in downstream= ( 6 + 2 ) km/hr = 8 km/hr Let the distance of the place be x km then, x/4+x/8 = 3hrs, x = 8km/hr