Boats and Streams is Based On Concepts of Speed,Time And Distance. Speed of river flowing either aides a swimmers ( boats ) while travelling with the direction of stream of river and opposes it when travelling against the direction of stream of river.

**Important Terms Used in Boats and Streams Problems :**

**Still Water :**If the speed of streams of river is zero

**Downstream Motion :**If the motion of swimmers ( boats ) is along the direction of stream of river

**Upstream Motion :**If the motion of swimmers ( boats ) is against the direction of stream of river

**Important Formulas Used in Boats and Streams Problems :**

Suppose If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

- speed of boat downstream = ( x + y ) km/h

- speed of boat upstream = ( x - y ) km/h

- speed of boat in still water ( x ) = 1 / 2 ( speed downstream + speed upstream ) km/h

- speed of stream ( y ) = 1 / 2 ( speed downstream - speed upstream )

**Shortcuts to Solve Questions on Boats and Streams :**

**Type 1 :**If speed of stream is x km/hr and a boat takes n times as long to row up to row down the river then,

Speed of boat in still water = x ( n + 1 ) / ( n+1) km / hr

Note : this is applicable only for equal distances

**Type 2 :**When the distance covered by boat in downstream is same as the distance covered by boat upstream.

The speed of boat in still water is x and speed of stream is y then ratio of time taken in going upstream and downstream is

Time taken in upstream : Time taken in Downstream = ( x + y ) / ( x - y )

**Type 3 :**A boat cover 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 the boat in still water is

Speed of Boat = y [ ( t2 + t1 ) / ( t2 – t1 ) ] km/ hr

**Type 4 :**A boat speed in still water is x km/hr and speed of stream is y km/hr it takes t time to travel to a place and come back again to starting position, then

Distance between two places is t ( x2 – y2 ) / 2x km

**Type 5 :**A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then

Distance is [ t (x2 – y2 ) ] / 2y km

**Type 6 :**If A boat speed in still water is a km/hr and river is flowing with a speed of b km/hr,then average speed in going to a place and coming back is [ ( a + b )( a - b) / a ] km / hr

**Type 7 :**If a person can row d

_{1}km upstream and e

_{1}km downstream in t

_{1}hours and also he can row d

_{2}km upstream and e

_{2}km downstream in t

_{2}hours then,

- Upstream speed of person = ( d
_{1}e_{2}- d_{2}e_{1}) / ( e_{2}t_{1}- e_{1}t_{2}) km / hr

- Downstream speed of person = ( d
_{1}e_{2}- d_{2}e_{1}) / ( d_{1}t_{2}- d_{2}t_{1}) km / hr

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