If you swim with the current in a river, your speed is increased by the speed of the water; if you swim against the current, your speed is decreased by the water's speed. the current in a river flows at 0.52 m/s. in still water you can swim at 1.73 m/s. if you swim downstream a certain distance, then back again upstream, how much longer, in percent, does it take compared to the same trip in still water?

11.23%

Explanation:

Lets take

Speed of man in still water =u= 1.73 m/s

Speed of flow of water = v=0.52 m/s

When swims in downward direction then speed of man = u + v

When swims in upward direction then speed of man = u - v

Lets time taken by man when he swims in downward direction is and when he swims in downward direction is

Lets distance is d and it will be remain constant in both the case

Time taken in still water

2 d= t x 1.73

t=1.15 x d sec

total time in current = 0.82 +0.44 d=1.26 d sec

So the percentage time

 Percentage time =11.32%

So it will take 11.32% more time as compare to still current.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s