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

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

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