ICOME
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Boat and Streams

Generally the speed of the boat or swimmer, means the speed of boat or swimmer in still water (speed of the water is 0km/hr).
Upstream → The movement of boat or swimmer is in opposite direction of stream (or against the stream) then it is called upstream movement .
Downstream : The movement of boat or swimmer is in the direction of stream (with the stream) then it is called downstream movement .
Let the speed of the boat or the the swimmer (in still water) is x and speed of the stream is y , then

upstream , the effective speed of the boat = x - y
downstream , the effective speed of the boat = x + y

Note : Let man's rate in still water x km/hr and speed of the current (or stream) is y km/hr .

then , x + y = man's rate with current (A)
and , x - y = man's rate against current (B)

x + y = A -------------(1)

x - y = B -----------------(2)

x =
1/2
(A + B)

x =
1/2
(man's rate with current + man's rate against the current)

y =
1/2
(man's rate with current - man's rate against the current)

So, we can say that

(a) A man's rate in still water is half the sum of his rates with and against the current .

(b) The rate of the current (or stream) is half the difference between the rates of with the current and against the current .