<PRE><B>Question 320479</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 x = rate of the current
and
5x = rate of the boat in still water
then
5x - x = 4x; effective rate upstream
and
5x + x = 6x; effective rate downstream
:
write a time equation, time = dist/speed
:
Upstream time + downstream time = 2.5 hrs
{{{12/4x}}} + {{{12/6x}}} = 2.5 hrs
reduce fractions
{{{3/x}}} + {{{2/x}}} = 2.5
{{{5/x}}} = 2.5
5 = 2.5x
x = {{{5/2.5}}}
x = 2 mph is the rate of the current
:
:
Check solution find the times; boat rate 2(5) = 10 mph
12/8 = 1.5 hr
12/12 = 1 hr
-------------
total: 2.5 hr
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