Boats and Streams

Boats and Streams

Boats and Streams Basic Concepts
• In water, the direction along the stream is called downstream.
• In water, the direction against the stream is called upstream.

Properties of Boats and stream
• You will be given the speed of the boat in still water and the speed of the stream. You have to find the time taken by boat to go upstream and downstream.
• You will be given the speed of the boat to go up and down the stream, you will be asked to find the speed of the boat in still water and speed of the stream.
• You will be given the speed of the boat in up and downstream and will be asked to find the average speed of the boat.
• You will be given the time taken by boat to reach a place in up and downstream and will be asked to find the distance to the place.

Basic Formulas • If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then
• Speed of boat in downstream = ( u +v ) km/hr
• Speed of boat in upstream = (u-v)km/hr
• If the speed downstream is a km/hr and the speed upstream is b km/hr, then
• Speed in still water = [(1 / 2) * (a +b)] km/hr
• Rate of stream = (1 / 2) * (a -b) km/hr

Example sum
If a man can swim downstream at 8 kmph and upstream at 4 kmph, find his speed instill water?
Speed downstream a = 8 kmph
Speed upstream b = 4 kmph
Speed in still water =[( 1/ 2) * (a + b) ]kmph
= [(1/2)*(8+4)] kmph
= ( 12/2) kmph
= 6 kmph
Speed in still water = 6 kmph

Basic Formulas
• Rate of stream=[( 1/2) (a- b)] km/hr

Example sum
A man can row upstream at 6 kmph and downstream at 10 kmph, find the speed of the stream?

Speed downstream a = 10 kmph
Speed upstream b = 6 kmph
Speed of the stream =[( 1/ 2) * (a - b) ]kmph
=[(1/2*(10-6)]kmph
= (4/2) kmph
= 2 kmph
Speed of the stream = 2 kmph

General Term:
Assume that a man can row at the speed of x km/hr in still water and he rows the same distance up and down in a
stream which flows at a rate of y km/hr. Then his average speed throughout the journey
= ( Speed downstream* Speed upstream )/ Speed in still water

 = [ (x + y) * (x- y)]/ x km/hr
Let the speed of a man in still water be x km/hr and the speed of a stream be y km/hr. If he takes t hours more in upstream than to go downstream for the same distance, the distance
= [ ((x2 - Y2 )*t)/ 2y] km

A man rows a certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of the stream is y km/hr, then the speed of the man in still water
=y*[(t2 +t1 ) / (t2 –t1 ) ] km/hr

A man can row a boat in still water at x km/hr in a stream flowing at y km/hr. If it takes him t hours to row a place and come back, then the distance between the two places

= [t*( x2 - y2 ) /2x] km

A man takes n times as long to row upstream as to row downstream the river.

If the speed of the man is x km/hr and the speed of the stream is y km/hr, then x=y*[(n+1)*(n-1)]

A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man in still water is given 

by = y* (( t2+ t1 ) / (t2 – t1 )) km / hr

A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes him t hours to row to a place and come back, then the distance between two places is given by

=t*(x2-y2)/2x

If Ratio of downstream and upstream speeds of a boat is a : b. Then ratio of time taken = b: a

Speed of stream = ((a - b) / ( a + b)) * Speed in still water.

Speed in still water = ((a + b) / (a - b)) * Speed of stream.

A man rows a certain distance downstream in x hrs and returns the same distance in y hrs. If the stream flows at the rate of z km/hr then the speed of the boat in still water is: Speed in still water
=[z*(x+y)]/(y-x)]