Question

It takes someone 6 hours to swim to a place against the flow and 4 hours to recover. Flow rate 3km / hr. How many kilometers does he swim in the still water?

Answer 1

Given :

Time taken to swim against the flow = 6 hours

Time taken to swim with the flow = 4 hours

The speed of flow = 3 km/h

To find :

Distance cover in still water

Solution :

Let The speed of flow = x = 3 km/h

The speed of man = y km/h

Let The distance cover while swimming = D km

∵ Distance = Speed × time

i.e Speed = $\dfrac{Distance}{Time}$

For against the flow

    x - y = $\dfrac{D}{6}$                 ..........1

For with the flow

   x + y = $\dfrac{D}{4}$                 ..........2

Solving eq 1 and eq 2

( x + y ) + ( x - y ) = $\dfrac{D}{6}$ + $\dfrac{D}{4}$

Or,  2 x  = $\dfrac{2D+3D}{12}$

Or, 2 × 3  = $\dfrac{5D}{12}$

Or,   6 = $\dfrac{5D}{12}$

∴      D = $\dfrac{72}{5}$  km

i.e  Distance = D = 14.4  km

Hence, The distance cover by him while swimming in still water is 14.4 km   Answer

 

Answer 2

Given : It takes someone 6 hours to swim to a place against the flow and 4 hours to recover.   Flow rate 3km / hr.

To find : How many kilometers per hour  does he swim in the still water

Solution:

Let Say Speed of Man in Still water  = M km/hr

Speed of Flow  =   3 km/hr

Distance covered against Flow =  ( M - 3) * 6   km

Distance covered with flow = (M + 3) * 4  km

(M - 3) * 6  = ( M + 3 ) * 4

=> (M - 3) * 3  = ( M + 3 ) * 2

=> 3M - 9 = 2M + 6

=> M = 15

Man Speed = 15 km /hr    in Still Water

Some additional info :

Time taken = 6 hr + 4 hr = 10 hr

Distance will be covered in Still Water in same time = 15 * 10 = 150 km

Distance of one side =  (M - 3) * 6 = (M + 3) * 4  =  72 km

Currently Distance covered = 72 + 72 = 144 km

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