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
