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 .