### Boats

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## Boat & Stream

Basic Concepts

A boat is said to go downstream, if the boat goes in the direction of stream.
A boat is said to go upstream, if the boat goes opposite to the direction of stream.

Basic Formulas

If speed of boat in still water is b km/hr and speed of stream is s km/hr,
* Speed of boat in downstream = (b + s) km/hr , since the boat goes with the stream of water.
* Speed of boat in upstream = (b - s) km/hr. The boat goes against the stream of water and hence its speed gets reduced.

Shortcuts

1. Given a boat travels downstream with speed d km/hr and it travels with speed u km/hr upstream. Find the speed of stream and speed of boat in still water.
b = (d + u)/2
s = (d - u)/2

2. A man can row a boat, certain distance downstream in td hours and returns the same distance upstream in tu hours. If the speed of stream is s km/h, then the speed of boat in still water is given by
b = [(tu + td) / (tu - td)] * s

3. A man can row in still water at b km/h. In a stream flowing at s km/h, if it takes him t hours to row to a place and come back, then the distance between two places, d is given by
Downstream: Let the time taken to go downstream be td
d = (b + s) * td

Upstream: Let the time taken to go upstream be tu
d = (b - s) * tu

OR
d = [t * (Speed to go downstream) * (Speed to go upstream)]/[2 * Speed of boat or man in still water]

4. A man can row in still water at b km/h. In a stream flowing at s km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance d is given by
d = [t * (Speed to go downstream) * (Speed to go upstream)] / [2 * Speed of still water]