<PRE><B>Question 1046114</B>
boat has a top speed of 6 miles per hour in still water.
 While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 30 miles downstream.
 Find the rate of the river current.
:
let c = the rate of the current
then
(6-c) = effective speed upstream
and
(6+c) = effective speed downstream
:
Write a time equation; time = dist/speed
:
time up = time down
{{{10/((6-c))}}} = {{{30/((6+c))}}}
cross multiply
10(6+c) = 30(6-c)
distribute
60 + 10c = 180 - 30c 
10c + 30c = 180 - 60
40c = 120
c = 120/40
c = 3 mph is the rate of the current
:
:
:
Check this; find the actual time each way
10/(6-3) = 3.33 hrs
30/(6+3) = 3.33 hrs</PRE>