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?

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