Boats And Streams Formulas

Formulas to Solve Boats and Streams Questions

1. What is Downstream: It is related to the direction of water flow in respect with the object, when the object or body is flowing in direction of stream it is called as Downstream

 2. What is Upstream : It is also related to the direction of water flow in respect with the object,  when the object or body is flowing in opposite direction then the stream is called upstream.

The boats and streams problems are based on the concepts of time, speed, and distance. However, a few adjustments need to be made in case of such problems. There are two variations of these problems.

Below are the best formulas needed to solve boats and Streams problems in seconds.

formulas for boats and streams

Basic Formulas for Upstream and Downstream

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 downstream = (u + v) km/hr
Speed 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 (a + b) km/hr  
2


Rate of stream

    1 (a – b) km/hr  
2

Lets 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 is :

    = (Speed Downstream)*(Speed Upstream)    
Speed in Still Water
    = (x + y)*(x – y)    
x

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 travelled is

    = (x2 – y2)*t    
2y

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)

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 is

    = t(x2 – y2   
2x
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