FOLLOW US:

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).

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Upstream → The movement of boat or swimmer is in opposite direction of stream (or against the stream) then it is called upstream movement .

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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 .

Tricks 1  A person can swim x km/h in still waters, and speed of stream is y km/h, it takes time t hours to swim to a place and back , the distance between the two places is

t(x² - y²)/2x

or

t(x-y)(x+y)/2x

Illustration A person can row 8 km/h in still water and speed of current is 1 km/h, How far is the place .

d =

t(x² - y²)/2x

= =

2(64 - 1)/16

=

2 x 63/16

d = 7.875 km

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Tricks 2 A person can swim a distance downstream in T_D hours and returns the same distance in T_U hrs(upstream) . The rate of current is y km/h , then the speed of person in still water is given by

y(T_U + T_D)/(T_U - T_D)

km/hr

Illustration A person can row a certain distance downstream in 4 hours and came back to original place in 6.5 hours . Speed of stream is 1.5 km/h . find the speed of person in still water

speed of person in still water is =

y(T_U + T_D)/(T_U - T_D)

(1.5)(10.5)/(2.5)

= 6.3 km/h

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Trick 3 A person can swim a distance downsteam in T_D hours and return the same distance in T_U hrs (upstream). The rate of person in still water is x km/h . Find the rate of current .

x(T_U - T_D)/(T_U + T_D)

km/h .

Illustration : A person swims from A to B (downstream) in 6 hours and from B to A (upstream) in 8 hours . person's speed in still water is 11 km/h . Find the speed of current .

11(2)/14

=

11/7

= 1.57 km/h .