Rivers Boats and streams

In Boats and stream based problems,we need to calculate either speed or time to reach some point either upstream or downstream.
Rivers Boats and streams


In water,the direction of the flow is downstream and opposite direction is upstream.



Speed of boat in still water is u and speed of stream is v then:
Speed upstream:u-v
speed downstream:u+v


If speed upstream is a and speed downstream is b then:
speed in still water is (a+b)/2
the rate of flow of the stream is (a-b)/2

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Rivers Boats and streams
Example1:
To find the rate of the stream, a man sails in a boat from location A to B at a speed of 12kmph and from B to A at a speed of 6kmph, find the rate of stream and speed of the boat in still water.
solution:
u=12
v=6
speed in still water=(a+b)/2 =(12+6)/2=9
rate of flow of stream=(a-b)/2=(12-6)/2=3
Rivers Boats and streams

Example2:
A man wants to reach from point A to B(distance b/w them is 6 km), he has two options to reach the destination the first one is to sail in the river and the second one is cycling.
A local person said that stream flow is 12kmph(A-B direction).If he uses a bicycle he can reach B at 12kmph.find the best suitable option for him.
solution:
If he sits in a boat it sails at 12kmph without any work and if he uses bicycle he can go at 12kmph but he has to work a lot hence boat could be the best possible option.





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