<PRE><B>Question 1015971</B>
The excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return.
 If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?
:
let c = rate of the current
then
5c = rate of the boat in still water
therefore
5c - c = 4c is the effective speed upstream
and
5c + c = 6c is the effective speed downstream
:
Write a time equation; time = dist/rate
up time + down time = 2.5 hrs
{{{12/(4c)}}} + {{{12/(6c)}}} = 2.5 is the equation we use to solve this
:
multiply equation by 12c
12c*{{{12/(4c)}}} + 12c{{{12/(6c)}}} = 12c(2.5)
cancel the denominators and you have
3(12) + 2(12) = 30c
36 + 24 = 30c
60 = 30c
c - 60/30
c = 2 mph is the rate of of the current</PRE>