Question

swimming downstream you can swim 2 miles in 40 minutes, and upstream you can swim 2 miles in 60 minutes...how long will it take you to swim one mile in still water?

Answer 1

Answer:

Vp = 1 / 24  miles/min   the speed in still water

Step-by-step explanation:

Lets call Vp speed of swimmer   and  Vw  speed of water then:

Downstream   Vp  +  Vw  

Swimmer does  2 miles in 40 minutes then he does

1  mile  in  20 minutes

Upstream     Vp - Vw

Swimmer does  2 miles in 60 minutes then he does

1 mile in 30 minutes

We get the following system:

(Vp  +  Vw )* 20  = 1    (1)         and

( Vp -  Vw )* 30   = 1    (2)

Solving the system

From equation (1)

20*Vp  +  20* Vw  =  1       ⇒     Vw  =  ( 1 - 20*Vp ) /20

Plugging that value in the second equation

(Vp  - Vw )* 30  = 1      ⇒  [ Vp - ( 1 - 20*Vp )/20 ] * 30  = 1

[20*Vp - 1 + 20*Vp ] * 30/20 = 1     ⇒ [ 40*Vp - 1 ] *30  =  20     or

 [ 40*Vp - 1 ] *3 = 2

120* Vp  - 3  = 2     ⇒   120*Vp  =  5   and   Vw  = 1 /120 miles/min

Vp  =  5 / 120 miles/min    or  

Vp = 1 / 24  miles/min

and speed of water   Vw  =  1 / 120