# Boat and Stream

Pratice Boat and Stream Questions and answers.

## Importance of "Boats and Streams"

Questions from the topic of 'Boats and Streams' are special type of ‘Time & distance’ questions. Questions from ‘Boats and Streams’ have been asked in different competitive examinations.

## Boats and Streams - Scope of Questions

Questions will be based on still water, down stream and upstream conditions. You will be asked to calculate the speed of boat/current swimmer, time in crossing and distance between two places.

## Boats and Streams - Way to Success

Ensure that you have understood the concept of downstream and upstream and also got expertise in solving questions from different ‘formulae’ and ‘rules’.

## Boats and Streams - Important Points

If the speed of certain boat in still water is v km/h and the speed of stream is u km/h.,then

• The speed of boat (downstream) = $(u + v)$ km/h.
• The speed of boat (upstream) = $(v – u)$ km/h.

## Boats and Streams - Important Rules and Shortcut Tricks

Rule Description
1

If the speed of a boat/boat/ship in the direction of stream (downstream) is x km/h and in the opposite direction of stream (upstream) is y km/h, then,

• Speed of boat = $\frac{x+y}{2}$ km/h
• Speed of stream = $\frac{x+y}{2}$ km/h
2

Let the speed of boat is x km/h and speed ofstream is y km/h. To travel d1 km downstream and d2 km upstream, the time taken is ‘t’ hours, then time will be

$t=\frac{d_1}{x+y}+\frac{d_2}{x-y}$

3

Let the speed of stream be y km/h and speed of boat be x km/h. A boat travels equal distance d upstream as well as down stream in ‘t’ hours, then the distance will be

$d=\frac{t\left(x^2-y^2\right)}{2x}$

4

If a boat takes time t1 to travel distance d1 downstream and time t2 to travel distance d2 upstream, then,

• Speed of boat = $\frac{d_1+d_2}{t_1+t_2}$
• Speed of stream = $\frac{d_1-d_2}{t_1+t_2}$
5

A boat travels a certain distance d upstream in t1 hours, while it takes t2 hours to travel same distance downstream, then,

$\frac{Speed \ of \ boat}{Speed \ of \ stream}=\frac{t_1+t_2}{t_1-t_2}$

6

If a boat takes same time t to travel d1 km downstream and d2 km upstream, then,

$\frac{Speed \ of \ boat}{Speed \ of \ stream}=\frac{d_1+d_2}{d_1-d_2}$

7

If a man or a boat covers x km distance in t1 hours downstream and covers the same distance in t2 hours upstream, then

• Speed of boat =

$\frac{x}{2}\left(\frac{1}{t_1}+\frac{1}{t_2}\right)$

• Speed of stream =

$\frac{x}{2}\left(\frac{1}{t_1}+\frac{1}{t_2}\right)$

8

If the speed of a boat in stillwater is a km/hr and river is flowing with a speed of b km/hr, then average speed in going to a certain place and coming back to starting point is given by

$\frac{(a+b)(a-b)}{a}$ km/hr