let

c = the speed of the current

v = the speed of the eight in still water

d1 = 3mi the distance upstream

t1 = 20 min = 20/60 hr = 1/3 hr the time of the travel upstream

d2 = 3 mi the distance downstream

t2 = 12 min = 12/60 hr = 1/5 hr the time of the travel downstream

since distance = speed*time we have:

the speed upstream is: v - c

(v - c)t1 = d1

(v - c)(1/3) = 3

the speed downstream is: v + c

(v + c)t2 = d2

(v + c)(1/5) = 3

by solving the system of equations:

(v - c)(1/3) = 3

(v + c)(1/5) = 3

we find:

v = 12 mph

c = 3 mph

click here to see the step by step solution of the system of equations:

the speed of the current is 3 miles per hour.

the speed of the eight is 12 miles per hour.