# Important Formulas - Boats and Streams - Tricks & Shortcuts

**1. Downstream/Upstream:**

In water,
the direction along the stream is called

**downstream**. And, the direction against the stream is called**upstream**.
2. 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**.

**3. 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.**

4. Assume that a man can row at the speed of

**in still water and he rows the same distance up and down in a stream which flows at a rate of**

*x km/hr***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**

5. 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

**= ((x**

^{2}-y^{2})t)/2y km6. A man rows a certain distance downstream in

**t**hours and returns the same distance upstream in

_{1}**t**hours. If the speed of the stream is

_{2}**y km/hr**, then the speed of the man in still water

**= y ((t**

_{2}+ t_{1})/ (t_{2}- t_{1})) km/hr7. 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 (x**

^{2}-y^{2}))/2x km8. 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))**

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Important Formulas - Boats and Streams - Tricks & Shortcuts
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