Boats and Streams

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Important definitions:

1) Downstream

In water, the direction along the stream is called downstream.

2) Upstream

In water, the direction against the stream is called upstream.

Some important formulae:

a)Let the speed of a boat in still water be x km/hr and the speed of the stream be y km/hr, then

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

b) Let the speed downstream be x km/hr and the speed upstream be y km/hr, then

Speed in still water =(1/2) ×  (x+y) km/hr
Rate of stream =(1/2) ×  (x-y) km/hr

c) 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

d) 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.

e) if the time taken by a boat or man is while moving upstream is double of what taken during downstream then the ratio between the speed of boat and the current will be 3:1.

  • Test 1

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